Evos are MUCH faster than 350Zs. Running at 100%, a completely stock Evo IX can hit high 12s. I believe in a recent issue of Speed magazine (from the editors and writers of Road & Track), they squeezed a 12.7-second quarter-mile time, which is amazing. The 350Z is capable of high 13s, but not much better. And the Evos can outhandle and outbrake them, too. But the 350Z is still an amazing car nonetheless, plus it has more sex appeal than an Evo does. And they aren't anymore high maintenance than 350Zs, which have even higher insurance rates, use similarly priced Brembo brake hardware, drink super unleaded gas and have similar fuel consumption, etc.
The V-6 does have potential, but it costs a lot to exploit it. You'd have to either do a lot of internal mods or use forced induction, neither of which comes cheap. The Evo, on the other hand, can generate around 60 awhp (which is 75+ hp at the crankshaft) reliably for less than $1,000.
I think the Evo is just as much of a sports car as the 350Z, if not more. The only difference to me is that it has four doors and a trunk that actually fits stuff in it. And maybe a little less sex appeal.