Cold air is denser, hence, it has more Oxygen molecules (which ecuates to more "usable" air). And the engine bay IS hot, so you want your air from OUTSIDE the engine bay. But again, the change in performance is not drastic...
As for changing the engine, it is cheaper still to just ad a supercharger with piggy back ECU than an engine swap. Engine swaps are expensive, time consuming, and a very involved project... Regearing is also expensive (at least $1,000 and on the cheap to have it proffessionally done on both axles). Also, keep in mind that one of the advantages of the 4 Banger is that it is light. It's not a bad engine either, if you gear it right and squeeze all the power out of it. It is reliable as heck!!!