I believe that Vereen was awfully capable in the blitz pickup while at Cal, and if I'm not mistaken, it was one of his pluses coming out of the draft. One would assume that he had some things to learn for the quicker speed of the pro game, but he was actually pretty decent coming out of the NCAAs.
As far as Vereen taking over for Woodhead, I think that Belichick typically leans towards the cheaper, younger competitor if he's fairly capable enough to handle the duties. This of course, saves us precious cap space, and we've seen it with Allen/Mesko, and Woodhead/Vereen lately.
Here is the comparison to see how it worked out:
Vereen 2013---47 catches, 3 TDs, and a 4.7 ypc ave on the ground
Woodhead 2012--40 catches, 3 TDs, and a 4.0 ypc ave on the ground
Of course the kicker is that Shane Vereen missed 50% (8 games) this season, while 2012 Woodhead didn't miss any at all. The point is that not only did Vereen outproduce Woodhead, he did it in a lesser amount of games by far. If he's able to stay healthy, he's the much better future prospect in my opinion, and the blitz pickup does play into that for sure.