Similar but not quite the same. The pitch attitude is referenced to the longitudinal axis of the aircraft and the wings themselves are generally set at a slight positive angle to the longitudinal axis. Also when flaps are extended the effective angle of incidence, which is the angle between the wing chord and the longitudinal axis, is increased. With flap deployed you can have a negative pitch attitude, ie slightly nose down, a positive angle of attack, and be in level flight. One of the effects of flap is to give a lower nose attitude for a given airspeed which improves forward visibility on the approach. So in level flight the pitch attitude approximates the angle of attack but there may be several degrees difference. In a climb or descent the attitude has no particular relationship to the angle of attack and in a fully developed stall the difference is drastic.
I’m not ignoring it - I said I’m not familiar with X-plane so I didn’t particularly want to speculate about how it works.
Flying outside the design envelope doesn’t necessarily break the flight model, it just adds error to whatever you’re evaluating. The further you extrapolate away from actual data, the less confidence you can have in your results.
During the test/experimental flights that an aircraft does to collect data to be used to build a simulator, the pilots will put the plane through all sorts of manoeuvrings that it will never see in service. They will put the plane into simple stalls and bring them back, but they will do so in clear skies, under controlled circumstances, using established procedures and following step-by-step methods where there are no surprises. The pilots - and sometimes the plane - will have a parachute, in case things go awry. They will hold a plane at the point of buffetting and collect that data. They won’t, however, go into deep stalls, or tail spins, or any other situation like that, because those generally aren’t recoverable and it’s a damn good way to die (see certification flights, CL-600, CL-604).
At this point in the simulator, the model isn’t broken, but it becomes theoretical. It is unsubstantiated by real-life data. We know a lot about airflows and airframe behaviour and moments and forces and whatnot, so we can still model things like “plane is oriented like A, wind going in B direction, rudder at C, ailerons at D, HSTAB at E, engines at F, so probably plane will orient to G.” The simulators will do this, and are often asked to do this, but the model is a mathematical one and it is (baring obvious variables: mass, wing length, airfoil profile, etc) the same for a Boeing 747 as it is for a Learjet 45. We know for a fact that those two planes don’t fly the same, but to some extent, outside the certification envelope they will be modeled in the same way. They have to be - because all we have are equations, not data, and those equations apply to either aircraft. This isn’t the same as an elemental analysis of airflow over wings, though - it’s a broader, more general calculation.
Again, simulators can be programmed with events from a crash sequence to evaluate the pilots, or the cockpit design or how procedures are followed, but they won’t tell you how the wind pushed the wing of an A330 in comparison with a B777 or whatever. You can get a simulator to do all sorts of things the plane would break apart doing: I’ve seen someone loop-the-loop a B747 around the Golden Gate Bridge. It worked because the calculations allowed it, not because the plane could actually do it (or maybe it could…I just wouldn’t trust a full flight simulator to determine whether or not it’s possible!)
As an example of something not being modeled in a sim, the BAe146 simulator we use doesn’t model ground effect, the increase in wing efficiency you get when close to the ground that tends to “cushion” the aircraft and arrest the rate of descent just prior to landing. As a result the aeroplane is harder to land nicely in the sim than in the real world. I don’t know if it was unable to be done at the time the sim was built or if it was deemed unnecessary, but it shows that the wing/air relationship isn’t being modeled directly.
Xplane does actually do a finite elemental analysis of the airflow they just call it “blade element simulation”, and it also models ground effect. They claim that based on the shape of the airframe and it wings, weight distribution, engine positions etc it can accurately predict how the plane will fly without having to have real world flight data entered into it.
They claim it is “more accurate” and they compare themselves favourably to other flight sim games such as Microsoft FS. The question is, is it accurate enough to model out of the envelope conditions to the point it can be certified by the FAA. The big issue is pilots may do deep stall training on a sim that uses theoretical data and learn a whole heap of stuff about flight in deep stall situations and then get themselves into an actual stall only to discover that there is some detail in the real aircraft that was neglected and that everything they learned was wrong. That is why theoretical data needs to be validated with real world testing. Simulators are procedural trainers and they don’t have to model outside of the envelope because if you find yourself in that position you have already failed the scenario and should not be continuing.
If you want better pilots who can handle unusual attitudes, send them up for advanced aerobatic training in a real aeroplane. What they learn there will be much more valuable than anything they learn by taking a sim beyond the known capabilities of the aircraft it is simulating.
Given how old the BAe aircraft are, there’s a good chance the computing power and sensor/data collection just couldn’t handle that much detail at the time the sims were built. Upgrades to sims are usually to bring them in line with upgrades to the aircraft, not to improve the simulator’s accuracy. There is a big difference between the older and newer sims in terms of computing power and feel: I’ve had the chance to be in both a CRJ200 and a B777 simulator - a few generations apart - and the difference is like the Super Nintendo to the PS3.
I once met a pilot who referred to full-slight sims as “death traps” because they are so unforgiving of errors and don’t take into account lots of little things, like in your example.
I suspect - but don’t know - that XPLANE and desktop simulators might be able to get Level A certification: to help with the fundamentals of flight and so on. Level D - the highest level, IIRC - are the full-flight simulators and I think they are largely considered to be fully equivalent to flight time on the real aircraft (for recurrent training, etc).
They are really cool video games too, and if I ever have a spare hangar and upwards of $10M to burn, I’d love to get one. 
The 146 sim is Level D. As you say, they are kind of considered to be time in a real aircraft. You can’t log the time as flight time, but you can log the instrument time as actual instrument time rather than simulated time, and you can do a full type rating in one. The first time you fly the real aircraft can be on a line flight with unsuspecting passengers (and a line training captain of course.) Level C sims can be used for the majority of your type rating but you have to do some circuits in the real aircraft as well
I’ve had a go in an A320 sim and I didn’t notice anything special about it, but then that aeroplane is quite old as well. The visuals in the sims I’ve been in have been recently updated with google earth data which makes it all look quite convincing. Too bad you spend most of the time at night and in cloud.
I’m in the middle of a four day training session now in the sim, and the trainer refers to it as a “fault amplifier”. Any small faults you have such as a slow instrument scan or a lack of finesse get amplified and made readily apparent for all to see.
I’m questioning now whether it has ground effect or not. Something does feel off about it and I was told by one of the check captains that it doesn’t model ground effect, but we did a wind sheer exercise last night and it certainly seemed like we got some ground effect helping us.
Do you ever get the time to try to loop it or whatever? If you asked the trainer (or whoever is in charge of the simulator) do you think they’d let you try?
The previous company I worked for had a pretty conservative view on that sort of thing. It was to be treated like a real aeroplane. Aside from that, one of the issues is that extreme attitudes can cause it to come off the hydraulic jacks. I’m not entirely sure exactly what that means as I haven’t seen it happen, but I know it requires a reset from the engineers so it takes time out of your $1000/hour sim session. My current employer has trainers who are more open to having a play. At the end of my initial type rating we did things like taking off from an aerodrome, flying at low level then doing a wing-over to reposition for a landing on the opposite runway, at the top of the wing-over three engines were failed and we had to get back to the runway on the remaining engine. We also set the weight of the aircraft very low, set the wind at 100 knots and hovered above the runway using thrust, pitch and roll to control our position, flying it a bit like a Harrier jumpjet.
Other than those bits and pieces it’s rare to have an opportunity to do anything more than the scheduled exercises. The time is expensive, we’re normally short on time anyway and if we do have time to spare most guys are more interested in looking at additional failures rather than just playing.
Richard - is there ever a situation where putting the nose down would cause a stall?
Technically yes, if you had negative g, say if you were flying inverted, then stall recovery is opposite and pushing the stick forward would cause or worsen the stall. In reality an airline pilot would never see a situation where pushing forward would cause a stall. Lowering the nose only to have the stall warning come on should cause you to disregard the warning but it just seemed to confuse them more.
The loop-the-looped 747 was being done by one of the motion engineers for the simulator. I don’t think coming off the jacks was much of a concern; those guys do shit like that all the damn time. They tend to try and one-up each other on various simulated stunts and weirdnesses. Or they freak each other out by logging in remotely and sounding random alarms (“RETARD RETARD RETARD”) at the wrong moments.
They also have their own version of the Vomit Comet… it’s not really zero g, though, but rather a vomitorium. They set up a simulator to respond to commands from a Wii-mote and let the thing bounce around like wild. I don’t think anyone’s dared to actual ride in it, though, because just looking at it while people are playing is enough to make your stomach heave 
It’s fun to have friends who build these things - I hear great stories!