Having just replaced a toilet for a friend yesterday, just wanted to plop in my observations here for those who might be looking to do the same.
The toilet being replaced was a low-flush one, not very old, but in a basement bath with a history of clogging problems. So my friend got a new low-flush unit which was supposed to be much better at disposing of waste. When I got a look at the tank I could see why: instead of the normal outlet and flapper, this one had a 4" opening, significantly larger. Which means that the water whooshes into the toilet a lot faster.
We'll see if it makes a difference.
I don't remember the make, but he got it at Home Despot, so I assume it's available pretty much anywhere.
One weird thing, though: instead of being at the bottom of the tank like you'd expect, the flapper sits a couple of inches up on an extension. This is obviously by design. Seems strange to leave that much water in the bottom of the tank; there must be some reason for this. (Hydrodynamics?)