Let me give my thoughts on the matter:
First of all, I assume the OP meant Kurt Angle in his prime, or Daniel Bryan in his prime, not how they both are at present, but there's a problem that arises with that comparison:
In Daniel Bryan's best matches, he was in the indy's and he obviously wrestled in that style. In Kurt Angle's best matches, he was in the WWE and he obviously wrestled in that style. These are two totally different entities since the indy's allow for far more technicality then the WWE, even in it's most technical time during the entertainment era (the era before PG and after Attitude). In this sense, it's not fair to compare Kurt's best to Bryan's best from a technical standpoint, since Bryan had more opportunity to show off his skills.
****Side Note**** We're obviously talking about PRO wrestling here, not Olympic style.
Now as for the Kurt Angle having sub-par psychology/storytelling point, I'll beg to differ slightly from Dub's point. First of all, we used the terms interchangeably in this thread and at least to me they are not the same thing. Kurt's storytelling is very solid. He can get the crowd to buy into everything he does, and his ability to work a match from point A to point B to point C, etc all the way to the end is very good. He's at least as good in that department as Rock, Cena (when he actually wants to), Hogan, Austin, etc. Where he lacks in storytelling is selling, something that guys like Punk, Benoit, and Bryan to a lesser extent are/were the absolute masters of. Kurt is 50/50 here, depending on who he wants to put over.
Where Kurt isn't great, or at least is inconsistent is, his in-ring psychology. The ability to feed off a crowd and give them exactly what they want to see. THIS is where the arbitrary grapple move in the middle/end match occurs. Sometimes it happens at the worst times too, times where the work rate is typically at it's highest, and Kurt will more or less do a rest hold.
However, when Kurt is at his peak, and everything is working for him, there's no one better (besides Benoit imo, but we won't get into that) and that includes Bryan.
With Bryan, I don't get where he can be considered boring in the very least, especially not coming from an avid Orton fan like IHV (for the record, I quite enjoy Orton, but he cannot compare to DB). Bryan has everything you want. Great storytelling, great moveset, high work-rate, the works. I don't know where someone can claim he's boring, but to each his own I suppose. As for mic work, Bryan's promos are actually pretty damn good imo. WAY better than when he first started, and you can see him getting more and more confident every week in this department. Bryan's also just recently acquired his main event status as well, so let's just wait and see where he ends up on the mic through the years.
The following is solely for IHV if he reads it:
You mentioned that you didn't see the story in the Sheamus vs Bryan match, but it's pretty easy to see if you were paying attention and actually looking for one, which I assume you really didn't. Going off of memory here, but if I recall Sheamus was over confident at the start, he just beat Bryan in 18 seconds, and he decides to play D-bryan's game. Sheamus goes technical, but Bryan is too nice, and Sheamus eventually gives up on it and goes back to his high energy physical style. Problem is, he's using way too much energy for the 2/3 falls type of match, and Bryan wheres him down with grapples and strikes, eventually working the arm to set up for the Yes Lock. Basically it was a match that DB controlled for the most part, as a way to put him over and keep him at main event status even through a loss.
As for Punk/Bryan, there wasn't much of a build for that one, so they basically just went out there put on a show. Bryan did work the back and the ribs, and Punk worked on Bryan's knee, but mostly that match was all about work-rate. Back and forth action to prove that neither one is really better than the other, setting up the rematch. Great psychology and awesome selling gave it the allusion of a story though, and that's all that really matters.