Wilcox rebounds and finishes around the rim. Birdman is an offensive liability.
Birdman is shooting 56.5% this year, shot 59.9% last year, and 56.6% the year before. So, yeah, he's not an offensive liability.
In fact, Birdman is stunningly similar to Wilcox. He is essentially a Wilcox-clone on offense who has serious athleticism and can throw down lobs with Rondo on the break and grabs offensive rebounds (11.7% career-- for comparison, Wilcox is at 10.4% this year). They also rack up defensive rebounds at a similar rate.
Their differences-- Birdman turns the ball over less (10.6% this year, Wilcox at 20.1% this year and 13.4% career) and gets a lot more blocks (a whopping 7.2% this year, 6.8% career-- for reference, Dwight Howard is at 4.5% blocks career). I'm not sure how great a team-defender Birdman is, but Wilcox hasn't been great on that front, so I consider it a wash.
If we could get Birdman for O'Neal and $3m cash (the max we're allowed to include), that would be perfect-- we would have two high-energy bigs to help on the boards. Trading Wilcox for Birdman is a little less optimal-- Birdman is basically a slightly better version of Wilcox, but with another two years on his contract (albeit at a reasonable price).