I've given some thought to this and conclude it's pretty much irrelevant. While I do think it will turn out Jon's the legitimate heir of Rhaegar, the Iron Throne's not really his thing. I also believe one or both of them will die in the final season. Don't expect Cersei to be totally defeated this season cause the focus is about to shift completely to the NK and his army of the dead. This is made obvious in the preview for week 5 so this next episode will be used to put all the pieces together in preparation for that big war.
No one knows for sure, as GRRM has never clarified where Bastards fall in the line of succession to the throne........
In order for Jon to clearly have a better claim than Dany, he has to not only be discovered as a son of Rhaegar and Lyanna, but his true parents must have also been married, removing his "bastard" status. If both things are found to be the case, Jon has the better claim*, as Westeros follows male-preference primogeniture succession laws.
Male-preference primogeniture succession means not only are Sons>Daughters, but sons of sons have a greater claim as well.
At question here is where in the order do the Male bastards fall? Naturally, they are at the end of the list of all the male siblings, but would a bastard such as Jon (unless found to be legitimate) precede a legitimate daughter, such as Dany? There is no answer to this question because GRRM hasn't weighed in.
Further complicating the issue is, Aerys II Targaryen, named Visery as his heir to the throne, skipping over Rhaegar, who in which would have been the rightful heir. It is unclear what this did to Rhaegar's heirs....of which Jon is one (presumably).
And then there is this vague statement made during the targaryen dynasty. "in the eyes of many, the Great Council of 101 AC thereby established an iron precedent on matters of succession: regardless of seniority, the Iron Throne of Westeros could not pass to a woman, nor through a woman to her male descendent's."
One thing we do know, that if we are following the Targaryen line of succession, and if Rhaegar and Lyanna did manage to get married, then Jon is the rightful heir.
But then there is still that pesky Night's watch oath Jon took.
Interestingly enough, the lines of succession so far in the show have all flowed through Robert Baretheon. And this is where things get interesting, because all the legitimate heirs that flow through Robert are dead, and one male bastard remains, Gendry.
