If I'm honest, most of the time there's no real discernible difference between FT output and the hardware render, especially with stuff that uses only the 2A03 (or the VRC6 or MMC5 expansions), but it's nice - at least for some people - to know your music can be successfully transferred onto the hardware FamiTracker is meant to imitate in software.
As I said above, VRC7 and N163 renders tend to be the most "interesting" (and therefore the most popular) due to the fact they are difficult chips to emulate faithfully, and they're the ones where FT output and hardware output might differ most.
Hardware renders are also a big help for debugging. I've helped pinpoint and fix a timing issue with VRC7 NSFs, find out what the average N163/2A03 volume balance is, fix a few DPCM issues in FT export... And many other things like this. Though to be honest, there are far better tools than a hardware NSF player to test and debug stuff on the NES (like the Power Pak for instance).
Actually I think the N163 is the least difficult to emulate faithfully. It's just the least pleasant to emulate faithfully. Really though, once it was properly reverse engineered it's the simplest of the chips.
I stand corrected. Nevertheless, I think people have a certain perverted desire to confirm that their N163 stuff does indeed sound horrible on the real hardware!
Really though, once it was properly reverse engineered it's the simplest of the chips.