32 bit software does not take advantage of the the 64 bit processing power. 64 bit computers will run 32 bit programs; but they will not run the old 16 bit legacy software.
If it were me, I would opt for the 64 bit Windows installation if
my computer and hardware were fully capable and I would install 64 bit programs when they are available. You may have some driver
problems with a 64 bit installation, which you can correct. If my computer and hardware were marginal, I would opt for a 32 bit installation.
Oh and if I install windows 7 ultimate 32 bit on a 64 bit pc will it run just as fast as on a 32 bit computer or slower?
That is a hard question to answer since "fast" depends on the processor speed, RAM, and hard drive speed.