For a toilet to work, it needs to get a siphon started. Older toilets tended to use lots of water in the bowl from the tank to get enough height to make it move fast enough to then actually start to siphon out. Newer toilets use a jet of water from the tank to get things moving MUCH faster, and without having to fill the bowl up first. Just dropping the amount of water into the bowl of an old design without a siphon jet just plain doesn't work well. It's not the tank that's the issue, it's the bowl. Most modern toilets still use a bigger tank than needed, since extra height helps with a bit more water pressure just like a water tower does...but, they shut the flush off by using a calibrated flapper valve, leaving a good portion of the water still in the tank. This has advantages other than just adding to the pressure - it means that there's likely a bunch of room-temperature water in there so when you flush and it refills, the cold water from the supply line is warmed up by the water left in the tank. Older toilets tended to empty the whole tank, so the entire thing ended up cold, and this caused the tank to sweat when the humidity was up, sometimes, even a little bit. While that can happen on a modern, low-flow toilet, it happens much less, and only in situations where the incoming water is quite cold, or the toilet gets flushed repeatedly before what's there can warm up to room temperature.