I'll give my opinion, though it is a bit of an evolving one, so take it for what it's worth.
First of all, I'm a recovering sting addict. I've tried figuratively everything at least once. I've mixed and matched strings from different sets and manufacturers, I've even been given promo copies from dealers...uh ... manufacturers. But, I've never seen a set of LaBella DB strings. Not at a jam session or a show. I've never had another bassist tell me they use them and I should check them out.
Tape wound are (I believe) unbowable, so anyone who wants to practice arco, or needs to play any, even the long root at the end of a ballad can't consider them. (Someone correct me)
Finally...I hate bringing this into this thread, but Mr. Carter isn't known for his tone the way that, say Sam Jones or Ray Brown is. I thought that he sounded great in the documentary and I attended a master class that he played in years ago where he sounded great. He is a wonderful player, but he made a lot of recordings, where it sounds like he went straight into the board to avoid bleed and that's just not a broadly appealing sound to bassists (engineers love it, though).
Everytime I hear Mingus I jones for gut strings, like any recovering addict. When I hear Mr. Carter, it makes me want to transcribe, but his sound ranges from "not what I'm going for" to "he sounds good on this one."