BB the GM is excellent at identifying where the game is headed so that he can acquire players to take advantages of those trends. No easy task in the salary cap era. Many teams just load up on doing what they do and hoping that to be good enough.
Not sure he is great at any of the 'Drafting/Contract negotiations/Player retention/etc.' you list - but he is excellent at combining them together and working the mid and lower 3rd of the roster to exploit weaknesses in others.
Sure Brady has covered up some of his weaknesses ... that can be said.
However - I think he knows Brady covers his weaknesses which allows him to gamble on player acquisition more than others. Not sure other coaches realize how to exploit their great players to shore up weaknesses that exist on their team.
I also think he is not vain in protecting any perceived reputation.
He moves on from his mistakes like they never existed in the first place ... and quickly.
The data indicates that BB is on par with other GMs with regards to the draft, but that he hits at about the same rate while having more picks. While dispelling the "BB drafts great!" myth, it is also a great argument about BB's ability to use the comp pick system, as well as about why he's so willing to trade down and into later years. I think this is one of several examples of why I think people on both sides of this debate miss the forest for the trees.
BB's free agency is obviously a very mixed bag. That's true at both the high and low ends. Anyone who wants to argue against that need only look at the list of free agent signings during BB's tenure. And a difficulty in being uber-consistent in FA is not some singular failure, as every GM is going to be inconsistent in FA, just as they'll be inconsistent in the draft. What happens here is that the homers ignore or minimize the Jordan Matthews/Donald Jones/Albert Haynesworth signings, while the eeyores will do the same with a Trent Brown or a Gilmore signing.
To me, UDFA is a thicker discussion, which needs to take into account situational falls (i.e. J.C. Jackson), level of play, overall success in the league, etc...) and is really worthy of it's own thread, so I'll leave it aside for the moment. If someone on either homer/eeyore side feels the need to argue it, they are more than welcome to do so.
As for the question I posed, I would argue, and many here have, and as you noted, that BB's greatest strength as a GM is also one that's sort of an umbrella strength, but one that flows in the opposite direction from your first offering (In other words, it's BB the GM following BB the coach, and not the other way around). And that is that he's willing to cut bait as fast as anyone, when it comes to a failed move/decision.
And the reason that I find that significant is that it's an inherent acknowledgment that he makes a lot of failed moves/decisions. Why is that significant to me? Because the homers mostly ignore the failure aspect, and the Eeyores mostly ignore the willingness to cut bait aspect.
Lastly, I've made the Brady point often, and I think that, like most other areas of BB the GM, it has a +/- feature to it, in terms of how we should assess credit/"blame". Having the G.O.A.T. to bail you out allows you to take risks you would never do under ordinary circumstances. On the other hand, BB's taken advantage of that to the tune of 9 SB visits and 6 SB wins, which is mighty damned impressive.
And that's really my point when it comes to the BB the GM threads. It's not a black and white issue, and one can make strong arguments AND rebuttals to any reasonable position taken in a "pro" or "con" direction. Unfortunately, rather than work the question from those types of reasonable positions, we tend to get either "BB sucks!" or
I'm always frustrated by the fans that whine about Belichick the GM when he is undoubtedly one of the best TEAM BUILDERS in all sports. This article captures his greatness.
The notion that Belichick the GM hurts Belichick the head coach is utterly preposterous.
when there's no question that BB does not suck as a GM, and there's also no question that, at times, BB the GM has, absolutely, hurt BB the coach.