Powder.exe uses neat instruction set extensions while Powder-legacy can't (since that's its entire point). Those extensions are often much faster than using without.
The sse2 version isn't really that much faster than the legacy version, but you should use the sse2 one anyway. I think the legacy one has some kind of bug (probably due to broken compiler optimizations or something) where particles move into walls and disappear.
One time someone complained that TPT didn't work on windows 98. I told them to stop using windows 98 ...
I really have no idea what it requires, but I do know I added a #define that made it target some version of Windows XP (can't remember if all Windows XP or just service pack 2). But everyone should really be using 7 or 8 by now ...
Edit: Also i'd also like to drop the -legacy version, it only creates confusion. For a game like TPT, extra optimizations make sense.