Then the Pats thought wrong (what a shock).
Not necessarily.
Hicks has been great as a DE in both Ryan's and Fangio's versions of a straight 3-4. He wasn't a fit in Allen's 4-3 in NOL, and he wouldn't necessarily be a good long term fit in the Pats' hybrid scheme (and maybe not a fit at all), where he'd likely be required to play more of an interior DL role as a DT.
It's possible that the Pats offered him what they thought he'd be worth in that role and that the Bears offered him more to play a different role in a different scheme. It's equally possible that Hicks himself preferred the 3-4 DE role over the role that the Pats would have him in and would've signed with a 3-4 team regardless. Chris Long pre-emptively turned down the Pats last spring because he preferred to play a different role in a different scheme (which is too bad, since he was excellent in the role that Pats had him playing). RJF did basically the same thing this spring, perhaps for similar reasons.
In any case, Brown has primarily played an "undertackle" DT role in the Pats scheme. It's not a particularly dynamic role and the assignments don't typically generate a lot of splash plays (which perhaps leads fans to believe that Brown is just not very good). And the undertackle role is most effective when working in tandem with a solid NT type (which the Pats didn't have last season). Brown has been a good fit for that role (a better fit than Hicks, perhaps) and has been very reliable and consistent in it.
But it's a completely different role from the far more dynamic role as a DE in the Ryan/Fangio version of the 3-4 - a role in which Hicks very apparently excels. For that reason, Hicks is worth more money in
that role than he would be if playing the undertackle-DT role.
I understand that a lot of people feel that Hicks is simply a "better player"compared to Brown, but it's a little like comparing Gronk to Shaq Mason. While Gronk may be "better" at playing TE than Mason is at RG, the roles aren't directly interchangeable (though they
do overlap occasionally on pulls and traps).
The bottom line for me is that it doesn't matter if Brown is the "best"
player compared to Hicks in a general sense. He's been the
right player (at the right cap cost) for the role he's been playing.