Bruce Bown is an excellent defender, but as others have pointed out, half of the story is that he plays dirty. Now, he's mostly just a dirty old man. Shane Battier is not even dirty. He can, however choke the life out of a guy's offense sometimes without even the opponent noticing it. Normally good offensive players end up 3 for 10 for the field and felt like you took 10 good shots. Even greats like Kobe end up taking something like 20 shots to get 22 points and go to the line significanly less often than he would have against a lesser guy. Shane is the true master of defense. We should refer to him as the Master Battier. The only guy I saw consistently beating Battier was Ron Artest. Not sure if Ron can do it as well any more. He seems to have lost a step.
Bowen is more versatile. He can guard point guards A LOT better than Battier. That is why I'd pick Bowen. Is he dirty? Yea. Hell yea. But you can't deny the fact that his defense is great.
The Master Battier swats shot (averages 1 per game, great for a perimeter player) and has the size to match bigger players (like Lebron James) better than Bruce Lee Bowen.
I think shane is a better defender if they both played fair, but bowen is better because of what he could get away with.
Shane. He practically invented the term "Hand in yo Face!" Check playoff videos of him guarding Kobe.