First off, let me tell you that the BC isn't completely software in the 80GB. Only the EE is emulated (but still uses the GS (Graphics Synthesizer) and other PS2 components.
Anyway, most games will have tiny issues regardless of SKU, so I personally wouldn't worry. Those I know of with an 80GB (and several PS2 games) say most every game they own plays fine, with maybe 2-3 with issues and one that doesn't work at all. Yes Sony updates it with every firmware, but I can warn you that while they may make improvements, some games may have new issues (not just with the 80GB, it happens with the 20GB and 60GB too). I just don't recommend getting a 60GB (people may say it has the best PS2 BC, but out of all the SKUs I've seen fail, it is by FAR the highest).
PS1 games are 100% software emulated and work similar to how they would on PS2 (the only thing is there's a tiny bit of input lag with the bluetooth controllers, because the timing in a game like Hot Shots Golf or any music game is a little off).