Both cars are fantastic.
The 370Z wins the look and sport compact feel - the tight cockpit and controls looks and feels amazing. The FR layout is great if you want a proper sports car, with the ability to let the rear slip occassionally. The looks is fantastic, it's the hard working middle class vehicle, people will start noticing you with smiles and thumbs up, it makes you stand out. Some even consider it "the poor man's Porsche" but I beg to differ. The VQ engine is very reliable and easy to moderate to maintain. I'd get at least with the sport package. For the power, it's pretty torquey (turkey? lol), but some may say not enough. What you have to realize is modding this car is different, some folks will say it's pricey but what you need to be aware of is that it's a car of it's own level, parts will not be cheap regardless if it's JDM or replica, it has that exclusitivity feel. It is also the first standard production vehicle to have a rev match feature for manual transmission available in sport package.
As for the Evo, it has tons of advantages as well - aside from the obvious 4 doors and a trunk, the All Wheel Drive system is extremely reliable and useful.
The turbo 4 banger at stock will feel okay, as for features, it's a rally car equipped with Recaro seats, fancy tach, brembo brakes and BBS wheels from factory. The aftermarket support for this vehicle is ridiculous, anything you can think of is most likely available. Despite what I mentioned, this vehicle will not feel high end, this is feed back from my buddies who have Evo 8 and Evo 10. One thing I like about Evos, with an cold air intake, exhaust and tune, this thing can eat the Z alive any day regardless if it's street or track, the ponnies goes instantly above 500HP with those ample mods. And if that doesn't impress you, my buddy's Evo 10 can eat Lambos which I think is amazing and retarded at the same time.
Carefully pick your poison, fantastic choices, completely different vehicles but both are amazing. Test drive both, for the Evo, Mistu has discontinued production I believe.
These are merely my opinions, good luck with your pick!