With CF wrapped barrels it's mostly about esthetics, as in they look cool, and, if you like the look of a larger contour barrel but you don't want the added weight of a larger contour a CF wrapped barrel is for you. Also, if you use suppressors and you want a larger muzzle diameter without the weight of a all steel barrel, CF wrapped barrel is an option.
There have been multiple tests done, one by a very reputable smith that frequently posts here, with regard to barrel flex and they've all shown the same results, two barrels of equal length and weight, one all steel the other CF wrapped, the equal length and weight all steel barrel had less flex than did the CF wrapped barrel. Doesn't mean a CF wrapped barrel still can't shoot good but the whole they're stiffer argument never holds water.
I have a few CF wrapped barrels, both, Proof Research and CA, because #1) I think they look cool. #2) I shoot everything suppressed and all my suppressors are DT so I like a larger muzzle diameter for them to tighten up against. #3) I just like how larger diameter contours look and if I can achieve that with a little less weight, great.
I did not purchase any CF wrapped barrel because I think they are stiffer, cool faster, or will shoot better than a all steel barrel. So far, I've been fortunate and all of mine have shot very well. I will say and this is after talking to a few different, very, reputable barrel companies, there is a higher risk in getting a barrel that doesn't shoot great with a CF wrapped barrel than there is with a all steel barrel. But, if don't mind spending twice as much, you like how they look, want a larger contour barrel but without the extra weight and you're willing to take the risk it may not shoot superbly a CF wrapped barrel could be for you.