I live in a twenty-story apartment building in a city.
Because the building has a water tower on the roof water pressure is very strong and, as a result, toilets are great. They flush like jet engines, can be flusher again immediately, and never get stuffed up or overflow.
Toilets in country homes are VERY different. You have to wait five minutes between flushes and getting stuffed and over-flowing are regular occurrences.
QUESTION: I may be moving to the country. I realize that nothing can make a country toilet the equal of one in a twenty-story building, but is there anything that could be done to make a country toilet at least somewhat closer to city toiler?
Caveat: I am not a plumber. 
My understanding is that the water pressure in the plumbing in your apartment probably has little, if nothing, to do with the strength of the flushing in your toilets (though it might influence how rapidly the tank refills). As I understand it, unless you have a commercial-style toilet (with no tank, and a breaker valve, like you see in public restrooms), the water pressure which is applied to a flush comes from the tank, not from the water line.
Older toilets, IME, are often very slow to fill their tanks, due to old, clogged inner piping.
I have a 1928-vintage toilet in the first floor of my house (original to the house), and that thing never clogs. I had the inner workings of the tank upgraded last year, and it now fills in about 2 minutes (it used to take more like 5).
In the U.S., the toilets that are really prone to clogging are the first-generation low-flow toilets, from the late '80s and '90s. In many cases, the toilet manufacturers reduced the amount of water those toilets use for a flush, without reworking the toilets themselves, which led to very weak flush pressure. Newer toilets use various techniques to generate a strong flush, such as Kohler toilets which have a pressure-assist system.
Most residential toilets don’t work any better when water pressure is stronger or weaker. The power of the flush comes from having a full tank, an unclogged roof vent, and a few other factors that have nothing to do with water pressure going to the residence.
I have worked in high rise buildings. on a tankless toilet extreamly low pressure can cause toilets to back up. They back up because the bowl does not fill properly and therefore will not properly siphon. Toilets back up because of what is thrown in the bowl, poor design, poor drainage, or poor venting.
to make your country toilet work as good as your city toilet don’t purchase a poorly designed toilet.
As a country person basically my entire life (at least 50 years of it) I have found 2 main causes of toilets backing up. Excessive use of toilet paper and a septic tank needing pumping. Toys and frozen drainage lines are very rare possibilities also. Compact solid stools sometimes take multiple flushes if not getting assisted getting broken up by the plunger. Tank refill time is a bit longer IMO in that pump pressure is usually a bit less than city lines. My switch is 40-60PSI so it is usually around 50-55 as that is what the pump can continuously maintain.
What you want is a “Pressure Assist” toilet. We had one from Toto that we called Supertoilet because it flushed so hard.
While a few respondents realized it, I should have said that the city toilet does NOT have a tank. It just has one pipe going into the wall from the flusher and one from the bottom of the toilet.
That’s what we had when I was growing up in NYC. No tank.
Anywhere there is lower pressure/smaller supply lines you’ll have a tank. Usually fed by a 3/8" or similar sized supply line.
Pressure assist toilets are good and flush with authority. The current crop of low water usage units can be good or bad depending on design.
I’ve got an American Standard Champion 4 that works very well. Not a single clog in the 3 years since it’s been installed.
How short a time between flushes is determined by your water pressure, supply line size and the inlet valve on the toilet.
If it’s a tank type toilet there not too much you can do about the inlet valve and line size.
Check out the pressure assist units. But the one I had years ago was kind of noisy.
Yup, and you’re not going to find that in a typical home because they require something like 1" piping, which for a house is usually the size of their entire water service. They’re also loud. The pressure assist toilet Pixel_Dent mentions is a relatively recent hybrid. They look like standard residential toilets with tanks, but inside the tank there’s another plastic tank that’s pressurized with both air and water in order to give the flush extra power. They use a standard size water line and still need some time to refill/recharge. They’re common in small commercial applications, but they’re still pretty loud so they’re not common in residential settings either.
Frankly, any modern toilet is going to flush quite well. It’s the first generation of low-flow models from the beginning of the 1.6 gallon era that suck. Since then manufacturers have done the proper engineering and every experience I’ve had with them is that they’re less likely to clog than the old ones, despite the reduced water volume. Toto is an excellent brand in that regard, pressure assist or not.
One of the toilets in my home is equipped with a Flushmate, which works well and saves water (although I don’t pay extra water taxes, so I have no idea why the previous owner installed it. ) https://www.flushmate.com/
I’ll confirm this with real life experience. When living in my old house, which had a well, we would sometimes lose power and, of course, the use of our well pump. We dealt with this by keeping 7-gallon plastic buckets filled with water under our back deck. If we lost power and water pressure, we would pour water into the toilet tank up to the regular fill line and then flush. The flushing action was EXACTLY the same, even though there was zero pressure in the water line to the toilet.
When we had our upstairs bathroom remodeled, ten years ago, we had a Kohler toilet put in. It’s a pressure-assist toilet, and works exactly as you describe (has the plastic tank inside of the porcelain tank).
Yes, it’s louder than a traditional toilet, but not obnoxiously so (IMO), and I think that the reliability of it is more than worth the bit of extra audio volume.
I was gonna mention pressure assisted toilets but since I was ninjad by about five hours, I’ll just post an article instead.
Part of the thing that might be helping in the apartment is that the waste lines have a big drop between floors. This allows the waste water to quickly move through the pipe. In a typical house, the waste line may be more horizontal and stuff will move slower. But toilet design also makes a big difference. Your city apartments may be more modern and have the latest designs. Country houses might have toilets which are decades old. Get a newer toilet and you’ll likely see big improvements. It seems crazy, but a modern low-flow toilets often work better than older, traditional toilets.
Anyone can use extra water to assist the flush.
Adding the water to the tank isn’t mandatory but convenient.
When we had work done on well/pump we would store water in the bathtub for flushing and just pour the water into the bowl. The bowl will siphon empty by this action so refilling bowl is easy just don’t add to much water as it will again siphon.
If there are little children around don’t keep water in tub and under deck either.
That is not a city toilet. But a toilet in a commercial building, one with a flushamoter. Can be the same kind of toilet but not with a tank. They both work the same.
I figured it had no tank when I read your post. If your water pressure is too low you could put in your own water tower
Are apartment buildings “commercial” buildings? Every apartment I’ve ever lived in or been in, in NYC, had no tanks on their toilets. I’ll admit that my experience goes back to the late 40s. This includes 3 story buildings that do not have a water tank on the roof.
I can’t recall the types of toilets in private homes at the time.
A great number of buildings in NYC do have water tanks.
I’ve noticed that a lot of hotels (or at least, the higher end ones) seem to have the pressure-assisted flush tanks. Not exactly sure how it works, but I assume after flushing, the incoming water fills an airtight tank until there is an air bubble at the top of the tank at the same pressure as the water mains. Then when you flush, this air pressure assists in the speed of the flush water.
Really old old-timey toilets had the tank up high (say 6 feet up or more) and a pull-chain to flush. I assume this also was to assist in the water pressure coming out for flushing. It is out of style because modern bowl-level(?) tanks provide adequate flush. Maintenance on a high tank could not have been fun.