There's a difference between a middling defensive player and a trainwreck defensive player. Hamilton is the former, Carlson is the latter.
Aside from that they aren't really that similar of a player. Hamilton is a much better puck-distributor and driver of offense (even if he doesn't personally score as much), while not forcing his partner to do all of the defensive lifting. He also tends to make his linemates better, while the same can't really be said about Carlson who seems to be the most difficult player on the blueline to play with.
As
@Hivemind mentioned my calculus wasn't just Hamilton > Carlson (though I think it's true), but that Hamilton + a haul > Carlson.
Perhaps Dougie was dead set on NJ and nothing could have been done to get him to DC. That's fine. I'm not saying GMBM messed up. There are too many unknowns to say that. I'm just saying I would have pursued Hamilton in a vacuum. He's one of the rare big-ticket UFAs who I think will end up being worth his contract, similar to Matt Niskanen.
I'm more interested in their overall philosophy going forward and how he truly assesses the team as it stands. If he thinks they are good enough as it stands now, then I'd call that a big mistake. But if he sees the team is lacking and is trying to address it then I think he's doing his job well. Typically he addresses team needs pretty well and pretty aggressively.