Type R:
Pro-- Lighter w/ better build quality than any Mitsu (previous owner of an '01 Eclipse). Much cheaper to both own and maintain.
Con-- FWD. AWD will almost always handle better, especially in the case of the Evo. If you're looking to mod, Evo will definitely keep the traction.
Evo:
Pro-- AWD and turbo. Excellent traction and handling. Evo is also much faster and will run mid-high 13's straight out of the box. Turbocharged engine and forged internals means you can up boost and get more hp cheaper than N/A.
Con-- AWD and turbo. Very expensive to maintain and more drivetrain parts to fix. Reliability and build quality have not been proven. You absolutely have to stay on top of the maintenance if you don't want stuff going wrong. Sticker price is already $10k-$15k higher than how much you would pay for an R... not counting the shitty markup all the dealers charge. Last con I'd have to say is that in the U.S., the differentials are crap compared to Japan. No limited-slip in the front, no Active Center Diff, and a simpler, less responsive limited-slip diff in the rear.