Like other people have said, boxing is limited. It’s really, really good at the type of fighting it’s tailored to: hitting people in the head with special gear. The gloves are heavy, which means that fighting without gloves is like running with a backpack; it’s ludicrously easy to do stuff without all that weight holding you back. Boxers are conditioned well and few real fights last longer than one boxing round. Boxers have killer combinations. If you let them get in close, they will hit, and hit, and hit, and you are not going to like it one bit. They hit hard. If they land even one punch, you’re pretty screwed because it will be followed by several more so fast that you’re probably not going to block them. Even if you hit a boxer, they’ll often shrug it off unless it was a really disabling shot to a vulnerable area because, like other have said, boxers get used to getting hit and dealing with it.
Drawbacks are that there’s no ref, there’s no bell at three minutes to give you a break, and you can’t clinch to rest. Also, as someone mentioned earlier, while with taping and gloves you can hit really, really hard, if you hit that hard without the tape and padding, you’re virtually guaranteed to break something. What I’ve heard happens to boxers in fights is that they hit one guy, abso*^¢#inglutely destroy that guy’s face…and break most of the bones in the hitting hand. They then get the crap kicked out of them by the guy’s buddies because they can’t use one of their hands anymore. Sure, they took the first guy out with no problem, but that didn’t help them win the fight.
Boxing, like other stylized and specialized sport fighting, limits target areas for safety. Boxers hit to the head almost exclusively, which can really hurt, but the head is armored pretty well and is instinctively protected well by most people. A real drawback to the boxer’s defensive posture is that it’s really ineffective without big padded gloves. There are gaps in the defense without gloves and it limits your field of view more than most other fighting defensive postures. If you get hit in your blocking hands, sometimes you actually whack yourself in the face, which is not as bad as taking the full force of the punch, but not real pleasant either.
In real fights you do not want to hit someone in the face with your fist very often, if at all. An open-hand push, palm strike, or even slap to the face are sometimes more effective – and always easier on your hands – than fists are. There are a lot better places to hit than the face, and most martial arts will teach you those. By learning good targets to hit you also learn what places are vulnerable to attack.
In general, cross-training is good. It covers up gaps in whatever other system you’re learning. You learn a different way of thinking for both attack and defense. I’ve met people who use one art to enhance another, like a guy who learned Tae Kwon Do to enhance his attacks for his main love, Aikido. He improved his understanding of both arts by training in different ways and shored up the weaknesses in each.
One problem with cross-training is that sometimes people don’t get into the art far enough to get all the mechanics and subtleties that make a big difference later on. Some of the really good Aikido or Judo guys can do a couple of tiny adjustments that turn a lock that less experienced guys can make only somewhat effective and painful into something excruciating, or make a throw seem effortless (to both observers and the poor sap who’s his training partner) when a beginner would struggle to not screw it up so completely that it doesn’t work at all.
Something to keep in mind if you cross train is that sometimes you have to stay with the mindset of the art you’re doing at the time. Being too soft in a striking art makes some of the techniques worthless, being too hard in a throwing art turns some of the really devastating locks and throws into total crap. After some experience with either, you can start to see where typical or traditional methods don’t work so well, but you really need some experience before you can make that call.
Some people were talking earlier about armed forces and police training. It’s rudimentary for most of the rank and file. One of the reasons some police end up beating a subject into submission and subsequently getting police brutality charges thrown at them is because they spend far more instruction in firearms than in submission, disarming, and restraint with a baton or unarmed. They also don’t have much required re-training time. Those skills need regular use or they deteriorate.
Armed forces spend minimal time training in unarmed combat because, realistically, unarmed-, bayonet-, or knife-combat in war is vanishingly rare. Special forces units get much more instruction, but even they will often supplement with civilian martial arts training in their off time. We had a few police officers and military guys who trained with us in my first dojo. Both police and military said the basic training was a joke compared to pretty much any quality martial arts training. The main advantage military guys had over civilians was the physical conditioning and the psychological edge of thinking they were bad boys. Police had more experience in defusing confrontations and in recognizing when things were about to get serious.