Maybe it's just that I've grown up on the NHL (EA) series, but I find that the scoring is semi-random in NHL 2K3. Goalies make some unbelievable saves sometimes, then let in some dude's wrist shot from the top of the circle.
It feels like the goalies were designed to compensate for a weak defensive AI. When I rented it, I always made these sweet plays with passes from a corner to a guy crashing the net, they NEVER worked (and they should, no goalie can stop those consistently). I started a short season while I had the game and only gave up 1 goal in 10 games (although it was on medium difficulty, not max).
That being said, I think that the more recent EA games have the same problem and are less realistic (more arcade-like) to boot. I don't know... I find that the simulation aspect of hockey games isn't that great, despite the fact that it's come a long way in the past few years.
<-- is holding out to see if the AI is better in the 2004 versions
As for game recommendations, no XBox is complete without Halo. Splinter Cell is a ton of fun as well and so is Rallisport Challenge.