The eMac is much better. But ask the seller if it has had problems in the past or if Apple fixed it. eMacs are known to get bad capacitors that can cause problems.
My eMac likes to shut itself off when a) It's not plugged in through a power strip and b) When it's in this one room in my house.
But nonetheless, it just randomly powers off, even during boot. I believed this to be a power board problem, but having read your post makes me wonder if it could be a bad capacitor? Is this a known symptom?
Ohh, and to OP:
Having purchased my eMac, I can say it was great for the 80 dollars I paid (shipping included with that price), but given the opportunity I wouldn't purchase another, not because of the above problems, but they're IMO just getting too outdated for Mac OS X. If your purchasing the fine PPC platform with intent to install Ubuntu on it then thats another thing, as 11.10 was just released for PPC and the support community is strong.
But, if your like me you purchase a Mac or build a Hackintosh for the sole purpose of using the Mac OS X Operating System and using all the one-of-a-kind applications known for the platform. In that case, Snow Leoapard, still practically a new Operating System, has lost apple's new iCloud support and now even MobileMe service ceases to exist. Leopard also has like no support, and is just going to continue to decline. And for the longest time I wanted a used iBook G4. But because of Apple's new strategy to push people to upgrade (No Siri for iPhone 4, even though the 4S is pretty much the same phone, No iCloud support on Snow Leopard, only 1 release old) I won't allow myself to purchase another PowerPC, unless for Ubuntu.
Don't get me wrong, PowerPC is a great platform, and the ones with the PowerMacs no doubt have years left on using them, but the eMac/iBooks struggle on today's internet, and the internet is just getting more bloated. Having said that, You can purchase a decent iMac intel from Newegg refurbished anywhere from 350 to 1000 dollars, be sure to get a core 2 duo as core duo won't support OS X Lion. Same goes with the Macbook.
I'm now personally saving for either a System76 laptop or a Macbook white refurb ($849 at apple).
Good Luck!