You said you’ll concede it by implying you’re too lazy to bother to put together a hypothetical build, not because you’ve come to realize you were wrong.
I am SO drunker than you.
I think I’m 75% drunker than you atm. 
Thanks, guys. I guess I’ll aim for the more expensive one and keep in mind the possibility of swapping out the graphics card if I still feel sluggish.
Is there another option besides those two? In either case you’ve got a mismatch - the processor is in a class several tiers above the video performance, and spending an extra $50 on the video will increase the total output well behind that as a fraction of the cost of the performance. Aiming for 5750 or GTX 460 level would be a good floor.
No, it’s Costco - they have like five desktop computers on the shelves at all, the other three of which are of the “check my email and surf the web” variety. I figure since I’m going from a five-year-old laptop to a newish desktop it will be a while before I get discontented with the new computer’s performance. I was going to just go for the cheaper one, but upon googling I ran across a thread at a build-your-own hobbyist’s site (Tom’s Hardware?) which basically said that integrated graphics chips were of the devil and I thought I’d double-check here.
The more expensive one will give you a much higher floor. You want to make sure the motherboard has a PCI-E x16 slot, that’s where you’ll plug a video card in. Some very cheap systems save a few bucks by not even having that slot to stick your own video card into. If you’ve got that, and a reasonable power supply (which also includes at least one PCI-e connector) you can always add a 5770 or 460 later if you find the performance to be inadequate.