I think you're confused. The 80GB model should be backwards compatible, it's just done via software emulation instead of having the old PSX and PS2 CPUs inside the system. So far as I know, only the 40GB model offers absolutely no backwards compatibility.
Personally, I'd keep the 60GB model. Last I really looked into it, the software emulation on the other models isn't quite up to snuff. The 60GB model should ensure near 100% compatibility with PSX and PS2 games, while the 80GB might only be 80-85% give or take a little. So even if you think there's a possibility of you wanting to play older games, I'd keep the 60GB model. There's also the matter of it being a lot easier to return the 80GB model, and not making your friend feel like they went to all that effort for nothing.
I'm deciding on which system to keep. I purchased the new 80GB at Sam's for $400, then found out it was not back compatible. Found a new 60GB (CECHA01) at a store in Tennessee and had a friend buy it for $500. I live in Florida, and now sit with both systems and don't know which one to keep. I like the idea of being able to play the old games on it, but don't know if my kids or I would as we will probably only want to play the newer hi-def stuff. I believe the old system has flash, sd, etc memory card slots and the new one doesn't. Also not sure if the older system has a dual shock control and/or wi/fi. I'm anxious to open up one of the boxes and start playing so would appreciate any advise.