I've been thru this last year. Paid about $200 (shipping included) for sony to send a refurb. The refurb was the exact same model (60GB BC launch unit made in japan) and looked brand spanking new minus the retail box. Came with 90 warranty. Turn around was about 1 week.
Had RE5 disc stuck in the thing and they sent it back along with the refurb console (you have to mention it in the form they make you fill out). There are some fixes for YLOD out there (such as adding thermal paste or replacing the laser) but doing so isn't a surefire thing, plus sony will not touch the unit even at your expense once that warranty sticker was been tampered.
It really depends how much you need the features on the classic console. Personally I don't use backwards compat, but it is nice to have if you ever feel like playing shaolin monks or other classic ps1/ps2 games without the bulk of a separate console. The extra 2 usb ports are nice, but i'm sure you can just get a hub if you require more. Aside from being more compact and using less power, the slims run a bit cooler and less noisy. Plus I think replacing the drive on the slim is much easier.
It's a bitch that a lot of the launch units seem to be affected by YLOD. Paid $750 for mine so definitely felt like a major kick in the nuts when it croaked.
As for backup, it may not be so easy. I'm not sure if new apps/tutorials have been released since last summer, but basically when I installed my ps3 harddrive into an external casing, it could not be read. The contents were either encrypted or was of some different file system that could not be seen on PC thru windows explorer. I also purchased one of those universal harddrive accesories, and that too could not decrypt the contents of the drive. In short, I wiped everything (including all my save date - playing thru RE5 again was a pain). The trophies data is stored online so that remained intact.
Perhaps you can do what tim mentioned - keep the hdrive and pop it into your new system and then do a backup thru xmb menu.
HOWEVER I recall at the time, if the console and the drive are not registered with each other, the system will do a complete format!
