I think Daenarys has displayed flaws that make her unworthy of the throne that Jon hasn't. As far as character purity, Jon should be the one. Daenarys has too much of a mean streak.
Being worthy is a rather mute point as GoT is really not a series that's centered around romantic notions like 'only who is worthy shall sit on the throne'. It's also highly subjective to decide who would be more worthy.
Daenerys is simply the only person in the world who has everything that is required to sit on the Iron Throne. She is the last real living member of the mightiest dynasty Westeros has ever known and who has ruled the land for over two and a half centuries. She had to flee at a very young age and was subjected almost her entire life to psychological and later also physical torture. Despite all of this and against all the odds she was able to resurrect three original dragons, raise up an army and pile up victory after victory.
The reality is that what Dany has done puts to shame almost all the accomplishments and victories other people achieved the past centuries and she did it faster while coming from much further. If Westeros would be at peace, her alienation from it would be a severe disadvantage as who would support a foreign ruler? However ever since Robert's death Westeros has been in complete chaos, resulting in many people suffering, both the nobility as the regular folk. This is one of the reasons why the Fate Militant has become so strong. Now a situation like that is ideal for Dany as she has never been poisoned by the politics of Westeros and she was able to gain both power and influence independently. To many people who are sick of the chaos, she would both resemble the stability of the Targaryen dynasty as someone who is free of the poisonous influence of the nobel houses. There would likely be quite a lot of people who immediately would support her just because she's different.
Purity and being meaning are irrelevant as pure people don't survive very long in King's Landing or have you forgotten Eddard Stark? To the world Jon is Eddard Stark's bastard from the north and now he possibly will become the self-proclaimed bastard of Rhaegar Targaryen who deserted from the Night's Watch to the Wildlings. Seen the political situation he could take the north as most of them hate the Boltons so much they're really not going to bother with a NW's deserter, but that really does not apply to the rest of Westeros. How could Jon ever take the Iron Throne? Something he doesn't even want.
Dany already said it last season: she's going to break the wheel. Purity doesn't get you the Iron Throne, fire and blood will.
The dragon has three heads. Daenerys has drogon. The other dragons are destined to be with others. If Jon is targaryen, then one of the others would be his. So there really wouldn't be a shortage on his side.
In other news, Ramsay vs Jon coming right up. We all know who is going to win. I just wonder how Ramsay will die. I hope it's by sansa's hands.
And Aegon also had only one dragon, but it was still him that was called the Conqueror, it was still him that rode the biggest of the three and it was still him that became king, not his two sisters.
So it's still very well Daenerys who resurrected three dragons, it's still very well she who is referred as the Mother of Dragons, it's still very well her who is riding the biggest of the three. So if Jon becomes a rider of one of the others (I always assumed it would be Viserion), it's really not going to be "Yeah Jon of course you can have one of my child-dragons and ride off with it and never return".
The other two dragons might be destined to be with other riders, but that only makes the possibility that Jon would serve under Daenarys that much more higher and realistic as those who are destined would be the closest ones to Daenerys.