I think MLB might be harder - simply because of my perception that players can play longer in that league - so there are fewer open positions.
OK - I looked it up. Average careers in each are 3.5 years in the NFL, 5.6 years in MLB, and NBA is 4.8 years. So players DO last longer in MLB.
When you combine the facts that the NFL has the largest rosters, AND has the most turnover - NFL has got to be the answer.