No, keep the PS3 you have. While the 60GB failure rate is still lower than some other console or even older PS consoles, it's more likely to happen because they are older consoles, have by far the most electrical components (more components usually means higher chance of failure), warranty is likely up (and if it breaks and you have no receipt to prove it was bought within a year, you gotta pay $150. Plus we've already had a few threads of broken 60GB consoles bought from CL and so on), and they dissipate more power (meaning they get hot much faster). 60GB consoles were last made in Feb./Mar. 2007 I believe. Not to scare people with the 60GB, but from what I've seen on various polls (of the SKU people own directly to failure), 60GB has by far the most failures. Personally, I feel its way too risky to get one. The 80GB with partial software BC is a better bet on lasting (I have yet to hear them have a yellow light error or blinking light error), but if I wasn't getting one new, I'd just avoid it personally (because if you buy new and have a receipt, you will at least have a year warranty).
Personally, PS2 BC is a mixed bag. While it can be nice having an all in one console and not having to use memory cards for saves, there are still some issues such as a little input lag, none of the SKUs have perfect PS2 BC (a firmware update CAN screw up a game's compatibility), some games upscaled and smooth actually look worse (PS2 games look the best on a PS2, connected to an SDTV), you are signed off of PSN when playing PS2 games (you have to reconnect the controller pressing the PS Button when first playing a PS2 game, and when you exit), and they take the longest time to boot up.
While I have a PS3 SKU with PS2 BC, I actually rather have one without, because it uses less power (and quieter), more likely to survive over time (my PS3 warranty is up), and so on. I only used my PS2 BC right when I got my PS3 near launch, but once I got my HDTV and more PS2 games, I just can't go back to playing PS2. The only thing I don't like is less USB ports, but oh course I can get a hub.
EDIT: Here is a thread over a CL situation on a 60GB
http://www.cheapassgamer.com/forums/showthread.php?t=198546
EDIT 2: It may be best you post this in the PS3 FAQ thread stickied, because that's where PS3 related questions are asked and answered.