I think a reasonable person without a dog in the hunt would agree that were Branch simply allowed to hold out the magic 10 games, his contributions late season and especially in the playoffs, say against the Colts, would have been a better course of action for the 2006 Patriots. Most probably would have resulted in another ring.
Long term +/- after that scenario is where I agree we have far more uncertainty.
Odds are he wouldn't have held out 10 weeks, either...
Long term +/- after that is where you either tag and trade him before the next draft or due to his performance (or lack thereof) you sign him for for more than you were previously willing to (or less than he was previously demanding) or let somone else have that pleasure...kinda like they did with Asante and the Eagles...
Thing is it's kind of like the Cassel situation dating back to 2006-2007 where people pointed to the fact that he was still here and not traded for value underscoring the fact he was worthless. While some of us pointed out the value he represented to Bill on the roster probably outweighed any trade value, which in fact became apparent early in the 2008 season...
A draft pick the following season can't generally provide enough value in season because it won't exist on the roster for at least another season... This season Mankins is of more value to them on the roster than another draft pick in a draft still a season away in which they already have 4 picks in the top 64. Sure they can plug Kaczur in, but as someone else pointed out his value (which his contract extension reflected) is in his potential versatility as an average starting RT or backup LT/G, not as a starting guard or above average tackle...
Had Mankins signed his tender last March after demanding a trade based on his now apparent unwillingness to extend at less than top of the position value, they probably could have facilitated one that would have landed them a pick that could have added a player like Asamoah, for example, to the 2010 roster. They didn't do that because they clearly had no idea what they were dealing with. They thought this was a rational guy who cared about where he played enough to be willing to negotiate towards a top 3 deal.
They do a pretty good job evaluating talent, although you could always do better. They don't always do a remotely good enough job evaluating intent. It's like that old adage about aging talent, better to move on a year early than a year late. Fool me once, shame on you. Fool me time and time again...shame on me.