I just reread about 30 posts over the last month on this topic. The reports on Branch are mixed, the most severe by Bedard in early June:
Deion Branch "continues to be unimpressive" in OTAs. "The guy catches everything but his burst is diminishing," adds Bedard. If not for Branch's mind-meld rapport with Tom Brady, it's unlikely he would have been re-signed after fading drastically down the stretch last season. Jabar Gaffney, spending most of his practice time behind Wes Welker in the slot, could begin eating into Branch's reps.
The last two days Branch has been dinged which doesn't help.
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BB favors the old vets many times, but the battle is not just Branch vs Stallworth. One also has to figure out the depth at all WR positions, and Branch seems like someone that would never be used at the X, and barely at the Z given the roster. While Branch knows all the positions he's behind the guys I listed at each position:
X (Lloyd, Stallworth, Gaffney, Slater); (forget Welker, Edelman and Branch here)
Y (Welker, Gaffney, AH, Branch, Edelman); (Stallworth and Slater don't fit)
Z (Gaffney, AH, Stallworth, Branch, Slater); (Welker and Edelman out)
When it's 5 wide, it's the starters at the three positions above + Gronk, AH.
If Stallworth continues to impress as he has and shows some more useable utility on ST then Branch - then BB going with Branch would seem to be putting his comfort ahead of the inputs.