Welker and Edelman are quite different players, probably because Welker is so unique.
Welker had the best acceleration I’ve seen, and as you recall early in his career he seemed to have superhuman burst as a punt returner. His top end speed wasn’t exceptional, but he was really quick to reach it. He used to just burst off the line like he already had a running start. It allowed him to often get wide open extremely fast, and often with a large degree of separation from defenders. He also used that acceleration immediately after the catch to gain huge YAC amounts. He was also so small it made him more difficult to cover.
I don’t know if Welker had better hands than Edelman. I actually would guess it’s Edelman based on my memory of the two. Welker was often so wide open that it makes sense his catch rate is much higher. However he had a noticeably small wingspan, and IIRC smaller hands too; Welker would often use his body to help corral passes and was able to get away with it because of the spacing. Brady used to also throw really low to Welker a lot, and he was great at catching balls close to the ground, bringing the ball in quickly to his chest.
Edelman is a lot bigger than Welker, especially in the lower body and just a lot stronger, and he has a much larger catch radius. You could think of him as a “more heavy version” almost like with a metal suit on. As such he doesn’t have the acceleration, but he’s harder to tackle, and more notably, he is a lot better with contested passes.
I think that “clutch play” is largely a facade in sports, but in this case you’d be really ignoring/not appreciating Edelman’s greatness if you can’t just acknowledge that Edelman is the guy you want in the waning moments of a Super Bowl if you could have either one. It isn’t so much a knock on Welker as an appreciation of JE. Belichick has said time and again he believes some players perform better in pressure situations than others.