Well, for 99% of your driving, even for aggressive driving, stock is fine. While some air filters are 'higher flow', higher than what? What's needed? Or just higher than stock? Think about it, with a modern FI engine, the limiting factor is the throttle body valve. Now, moving a source of resistance to the air out to the filter is not exactly the same thing, but it would make essentially no difference in performance from what you'd see except for WOT. (Wide Open Throttle) And even there it would be VERY marginal. Remember, the computer is going to adjust everything to where it should be all the time.
In most cases...
Turns out that with SOME vehicles there are some things you can do about performance at WOT. Dodge Intrepids, and similar, for one thing, have a reputation (with the 3.5L motor) of being 'restricted' at WOT due to the air box at the fender well. (They are designed to draw 'outside cool air', not hot/warm air from the engine compartment) Anyway, they have a reputation of a noticeable power benefit from modification to that area. (And a lot more intake noise as well! Seems the air box was designed to limit intake noise.) The air box mods didn't seem to do much with the 3.3L motor setup. And it didn't seem to affect mileage, only WOT performance. Later Intrepids didn't seem to be affected the same way, or so the rumors go.
A lot of this is hype though, as back in the 60's there were a lot of issues with intakes. My brother, for example, took the top of the air cleaner off on a Buick Skylark 350 V8. In it's place he got a 'flat' disk that screwed down and exposed the air filter all around instead of through the air duct. In cold weather warm-ups were a problem (it no longer took air over the exhaust manifold when cold to assist in warm-up) but other than that, it didn't seem to affect normal driving. Made an INCREDIBLE noise when you stomped on it, and he claimed better ETs, but I never saw the numbers. However, remember that this was before computers.
Bottom line? Most of anything you do, unless it starts bumping 'limits', is just going to be compensated out by the vehicles computer. That's not to say it's a bad thing, just that you probably won't notice much difference.
As to changing from 'cold air' to engine compartment 'warm air', I don't think that would generically be a good thing. But again, I don't think you'd see that much difference in normal driving.
Hmm, can you put a 'box' around the new filter and duct it to the old cold air intake?