In determining who has the best claim on the iron throne by right of birth there are multiple factors involved.
If it's just between Jon and Aegon first it boils down to if Aegon is the Aegon (Rhaegar and Elia's Aegon) he claims to be (unlikely). Aegon would have the better claim. However there are serious doubt he's Rhaegar and Elia's Aegon and not another Aegon from a different branch of the family tree.
If we go for who has the overall best claim to the throne we have two major hic-ups in forming succession, The Dance with Dragons and the Blackfyre Rebellion.
Basically the Dance with Dragons left Westeros with a rule that female claims came only after male claims with regards to the throne. It is unclear, however, 1) how far through the family tree does it stretch is it son, son, daughter, brother, brother, sister, uncle, uncle, aunt, great uncle, great uncle, great aunt ect. or does it go son, son, brother, brother, uncle, uncle, great uncle, great uncle, daughter. Also then does it merely apply to female persons themselves or does it eliminate their children as well. (son, son, daughter's son, brother, brother, sister's son ect. or son, son, brother, brother, daughter's son)
Then there's untangling the succession of Aegon the Unworthy. Given he legitimized all his kids we don't know if the succession should have gone by birth order or if his trueborn son was actually his son (given Bloodraven put his support behind Daeron II I'm sure that Bloodraven probably had proof Daeron was the real deal).
Finally there's the issue that we don't know what happened to certain branches of the Targaryen line. Aerion Brightflame had an infant son who was passed over on account of a)being a baby and b)being the son of a mad targ prince. We don't know what happened to the son or any decendants. Aerion's elder brother had a "half-wit" daughter we don't know if she married or had children. We don't know about any female blackfyre lines or about any decendents of the prince of dragonflies.