DX11/Eyefinity = damned near useless on a low class card. That is, unless you plan to run on triple 17" monitors. You'll still be able to use two monitors on the 4670 though.
I do not recommend multi monitor setups actually under normal situations (from personal experience, I now believe a single 30" is superior to 3x 23").
The 5570 will run cooler, but the 4670 will be cheaper. Doesn't really matter which card you get though.
Mid-end last gen card vs. low-end new gen card = tie.