I can see bits & pieces that are similar but, overall, I don't see much of a resemblance.
Like Angle, Bryan is currently doing something of a nice guy bit, but he's doing it in a more realistic way. Angle would go on and on about his accomplishments, especially winning the gold medal, like an arrogant buffoon that believed he wasn't being the least bit cocky and that he was just a "nice guy". Bryan's situation is that of a guy that almost seems like he's being misunderstood due to curcimstances and points of view. For instance, Bryan saying that Big Show intentionally ran over AJ as he was so focused on taking the title from Bryan does have a ring of truth to it. Is it true? Not at all, and people know that & boo Bryan for suggesting it by feeling that it's a means of putting Show down while avoiding the issue that he might have been close to losing his title. At the same time, when you look back over the course of their feud, Show has obviously been frustrated at his short title run, Bryan having the title and not being able to take it from him thus far. So him being so reckless that he ignored AJ's safety isn't impossible. Unlikely, but not impossible.
Trying to build Bryan in the same way as Angle may not have worked. At the time when Angle first showed up, the WWE used the fact that he was this highly decorated amateur wrestler that won a gold medal at the Olympics. That he sometimes competed and fought through tremendous injury for the sake of being the best. Daniel Bryan, on the other hand, is a veteran of the indy circuit that stands under 6 feet tall and weighs about 200-210 pounds. Angle, on the other hand, was a very muscular 250 when he began his career as a pro wrestler. Also, they didn't start Kurt Angle out feuding with men 200 pounds heavier than he was after he won his first World Championship. It's believable to see Bryan having to resort to using everything he has to beat the likes of Show & Henry. He has to use his athleticism, his superior wrestling knowledge and even a little cunning to overcome the fact that he's so much smaller & physically weaker than his opponents. He can't just stand in the middle of the ring and trade haymakers with those two. It'd look ridiculous and not the least bit believable. Believability has been the key, thus far, to the success of Bryan's slow transformation into a heel, believability was key to Mark Henry's incredible success & dominant title run since last summer and the believability they've generated in the big man vs. little man scenario has helped all these matches tell great stories.