I honestly don't put a ton of stock in analytic numbers unless you're comparing two similar players who are deployed similarly. I would rather watch the players. Brodin and Brodie are both guys who can be beaten one-on-one, especially by physical forwards. Both of them are decidedly unphysical and are routinely overpowered in the crease and along the boards. Neither block shots very well, though both are good positionally and in gap control, which certainly deter shots from being taken.
Though Brodie is decidedly an asset with the puck on his stick, Brodin is not. Brodin is solid with an outlet pass and makes smart decisions with the puck, but he lacks any discernible vision, while Brodie's vision is good. But Brodie is also prone to the occasional poor play with the puck, while Brodin rarely makes those types of mistakes. Brodin's weakness is simply that he is not very difficult to beat down low, especially if you're a physical forward who can intimidate him into giving you too much space.
Why are these two getting shopped? Well, in Brodie's case it's that Rasmus Andersson replaced him as Mark Giordano's sidekick, and outplayed him as such. Brodie is a serviceable 4/5 defenseman with one year left on his contract at $4.6 million (with a NMC), which the Flames would like to unload because he's not discernibly better than Andersson -- plus, they believe that Valimaki and Kylington can easily fill his role as the Flames' #3 LD behind Hanifin and Andersson.
As for Brodin, it's more difficult to pinpoint, since the Minnesota GM (Paul Fenton) has proven to be both unpredictable and not very competent (Niederreiter for Rask, straight up, cough cough). It is certainly fact that Minnesota looked pretty good last year until Matthew Dumba was injured and the blueline began to show cracks. Suter and Spugeon were excellent as always, but the defense core behind them was routinely dominated by opposing forwards. Still, I don't see why Fenton would shop Brodin -- the Wild LD is very thin behind Suter and he's a solid 4/5 D whose contract is only slightly too high at $4.1 million for two more seasons.
I agree with you that analytics are too often used as a substitute for analysis. It's tough for me to believe that people would want to give up valuable assets to acquire a player like Brodin or Brodie who would do nothing to address the major problems concerning the Devils blueline: too soft, too small, routinely pushed around, not fast enough, no big point shot, etc. Neither Brodin nor Brodie has a singular dynamic skill whatsoever. Better to give Smith and Davies that ice time -- even though they might make rookie mistakes, at least there's discernible upside there at the end of the rainbow. With Brodin and Brodie what you see is what you get, and it's not very much.