Ok, can only give comparison on bait
My flies have always been singles. I fished only a couple times in UK, and can't remember if I was using a single, double, or treble.
But, when I first started steelheading. We used treble hooks with our bait and on our plugs. Some guys when allowed still use trebles on plugs. I've noticed, that on bait hookup/land ration was MUCH higher. I mean, only time you'd lose a fish was if it ran into trees/obstructions. But, with our sandshrimp or eggs, the fish would engulf it, and would always have 2-3 of the hooks into the fish. When they outlawed trebles, and went down to singles, our catch rates went down. I believe sometimes the fish would grab hook just right or off to side and hookset pulled hook out or impaled into a soft place. Lost more fish in that regards. Had almost no difference between barbed and barbless. Normally the barbless would sink faster and deeper with less effort. Only on the constanst acrobatics of some fish did they ever toss a hook. With fly fishing, I'd have to assume similar things would transpire. If you have a solid hookset, your single will drive in deeper. BUT, you'll have more of a pivot if you're using longer hooks. I'd assume if you had 2-3 of your treble hooks in with a longer hook, would be tougher to maneuver out on the leverage point. I only use singles/siwashes nowadays. I do know that in the days I used trebles, if that plug went off, I got the fish to the boat everytime. The only time I lost a fish was when I lost plug as well on a snag. Period! You do have guys who like to use oversized trebles on plugs, which cause a snagging effect if run into fishing zones. I never did that, nor did my fishing partners. I have had WAY too many times having fish spit or miss hooks hitting with siwashes on. I can't count how many long lined releases I've had on siwashes rather then trebles (none with trebles).
As I said, mine is more from a conventional gear aspect. It's a different fishing style. Especially with bait. With flies, I couldn't give a fair assessment, since I don't recall ever using them. But, hope my conventional gear assessment helped.