For me, AJ has always been the equivalent of HBK, but for the current era. - Allow me to explain; back in the day HBK was the smaller main event guy that was flying around and putting on ridiculously good matches but, for me, never was much of a promo. And that's where AJ is.
The difference is that AJ had that Phenomenal run of work through the X-Division into the heavyweight picture in TNA where everybody could see he was special but he never seemed to get enough time to prove it. And then he went to New Japan and did just that.
Michaels for his part has been involved in some good moments, including probably one of the most remembered of all time when Marty Jannety tried to dive through the barber shop window to escape from him and had a good, cocky character, but I don't think his body of work holds up to Styles - certainly in the style that the majority of modern fans might find entertaining.
Having said that, HBK makes for a more engaging character - but for a one off dream match, that's kind of irrelevant (IMO)
For me, Styles is the best in ring wrestler of the modern era. Better than Bryan, better than Michaels and right up there with the likes of Bret Hart and Benoit, and for that reason, I put Styles over.