I think Jon will instantly dislike Aegon because the boy is a brash, spoiled brat that still smells of summer, while he is much mature because of the experiences that he has been through, and the fact that Jon is carrying the burden of the world on his shoulders.
IMO, I doubt they ever meet; considering Dance 2.0(Dany/Aegon) most likely happens before anyone learns of Jon parentage, unless the real Dance is between Dany/Jon. Either way Aegon, most likely will be gone before then(sad to say that, because he actually could help Westeros.)
All that said, IMO Jon would not "dislike" him should they meet. Jon has shown plenty of times that he has one of the most progressive minds in the series. I equate his stance on the Wlidlings, to that of Dany's stance on slavery(despite my personal feelings about her.) He may dislike the way Aegon, goes about handling matters; but Aegon is not a Bolton, Frey or certain Lannisters. Furthermore, if Jon actually believes they are both of same biological father; I doubt he would dislike/hate Aegon. That being said, should Aegon make his way north and the conflict directly endangers or harms Rickkon, Sansa, Arya or Bran(unlikely) AND Jon can directly tie Aegon to it....well, all bets are off then.
I'd also like to add, that I don't get how Aegon gets this "spoiled brat" rap. Because he acted like a punk, in front of Tyrion? How do we know he wasn't playing Tyrion, at that point? Possibly to show a bit of that Targ "anger" BS. The kid was brought up in the company of mercenaries, in a less than hospitable region. At some point he had to have been bloodied in a skirmish. He was given an education and groomed to lead..without the comfort of a damn palace.
Despite all I just posted, I still believe him to be a fake.
Edited by Northbound2.0, 31 January 2014 - 05:34 PM.