I try to do this like a math problem so here is what I have so far:
Speed: Tie
Bradley is faster in part because he's smaller but also because he's just one of the fastest guys in the NBA. Shumpert ran a 3.18 and Bradley ran a 3.14 in the 3/4 court sprints. That is to say that it's negligible.
Height: Shumpert
This is where I start thinking that Shump might be worth Bradley. He's got a ton of talent and he's taller than Bradley but about 3 inches. That means he can play 3 positions in a pinch. Also, and I have no stats for this, but his has a better handle than Bradley from what I've seen.
Defense: Bradley
He's just shown more so far. I've obviously watched more Celtics games than Knicks games but I haven't ever seen a game where Shumpert made the kind of difference that Bradley has. Bradley took a championship caliber team and made them better.
Injury History: Tie
This was a tough one. Bradley has had more injuries, ankle surgery and two shoulders but Shumpert had the dreaded ACL tear in his 1st season which is pretty tough to swallow. For a defensive minded guard I'd rather have Bradley's history. I called it a tie because it's a gut call.
Attitude: Bradley
This is more of a subjective category. I personally don't like a lot of bragging or egotism. Shumpert is a lot more hot-blooded while Bradley is very cool-headed. I tend to prefer the guys who are quiet killers. It's one of the reasons I love Rondo so much. Dude is 2nd all time in playoff triple doubles but in the post games you hear him talking about how great Marquis Daniels played. Go figure.
So despite Shumpert being really impressive in his rookie campaign and taller, I really can't talk myself into giving up Bradley.