To follow-up nikwax.
Yes, you'll need to do all four tires, especially when changing the general tire type. Otherwise you can really screw up the handling at the limit. You might not see it driving around, but that critical stop in wet weather or quick turn to avoid another car could turn out much worse than expected if you mount dissimilar tires.
Tire won't make it a dragster, but the Ecopia's do compromise grip for the sake of range. All the tires in the above discussions should improve dry (and probably wet) traction thus improving acceleration, deceleration, and turning performance. I can't say how much you'd notice the change, and it certainly depends on the tire, but I would expect 1) more cornering grip in a hard turn, 2) better hook-up and acceleration from a low speed, 3) better feel for the tire's adhesion limits in a turn and 4) better braking performance. All of this with less squealing from the tires. I don't know how much, say, the Michelin Premier's would improve 0-30 or 0-60 acceleration runs but I'm confident they won't hurt!
I'll also note that just flooring the throttle will not necessarily be the fastest launch. Typically keeping the tires at the limit of adhesion; but not spinning, hopping or activating traction control; will be the fastest.
