The 203w power brick will work on all Xbox 360s. The 150w power brick will only work on Jasper 360s. Using a 203w power brick on a Jasper 360 will only (theoretically) draw 150w from the mains. The only downside is that it will be older, bigger, and potentially noisier (although in my experience, the 175w power bricks are the noisiest... maybe just the dust).
The power bricks are designed not to plug into any Xbox that has a higher power requirement than it can handle, because it simply would not work. If you can plug it in, then it'll work fine. There are no real side-effects (although you may prefer using the 150w brick for Jaspers simply because they're nice and small and don't get in the way so much).