The technique BluePhaze said should work fine in both CC and C2, what he's referring to as "IE" is Internet Explorer, for when you export a game from Construct 2. At the moment Construct 2 gamepad should only work in Google Chrome web browser I believe.
Construct Classic should work fine for 360 controllers as long as the game itself runs (meaning the computer you run it on has Windows and DirectX9 (free) usually)