The first example comes from Resistance: Fall of Man which shows no blood when run on a Japanese system but lots of blood when run on a US system. Also, it doesn't matter if you have the Japanese print or the US print of the game, as it's built into both.

The second, which also comes from Resistance, is a bit more of a concern for online players. Your console's region essentially pairs you with that region's online servers. Thus if you have a Japanese system and you're playing Resistance online, you'll be playing against Japanese gamers. And well, they're a lot easier to kill :P.