Picks do have some effect on your tone. I use Dunlop 1mm nylon picks. If I go lighter the tone changes and the feel changes. The lighter I go, the more the tone varies. Extreme example - tone is not the same with a Dunlop 1mm as with a red sharkfin.
Again there is no "right" or "wrong" here. It's a matter of what floats your boat or the best compromise
for you.
There may be another aspect to this as well. Richard Thompson finds they tire you out more over a show. I should point out that he does 1.5 to 2 hour shows, makes virtually non-stop use of hybrid picking live, and that when I showed that technique to my physio she said "that's a good way to wreck your elbow" so this may be a case of aggravating an injury (he seems to have quite a lot of problems with his right elbow, reportedly icing it baseball pitcher style after shows)
I use Gibson teardrop medium gauge, what used to be the "Les Paul" pick. These are harder to get now, but Fender make an equivalent. I truly prefer a heavy gauge pick, and sometimes use Fender heavies in the studio. I find that the tone is better, but playing with that for a whole show tires my arm out.