It'd change the line of succession away from Tiberius (who Augustus never wanted anyway).
This would mean no Caligula and no Nero, and potentially more importantly no Claudius.
That said, after Augustus, with a brief respite with Claudius, it went to hell in a hand basket pretty fast anyway until Vespasian. Who knows, it might not have made much of a difference as long as some half competent Flavian was waiting in the wings to take over when a Julio-Claudian died childless.
Or....we might still be living in the Julio-Claudian dynasty now. Augustus was a pretty smart guy, so he probably would have been able to train a heir well (this issue was, of course that they kept dying and he had to plump for Tiberius).
In general (with the exception of Alexander Severus) young and inexperienced men make horrible Emperors. If Augustus was able to have a son and still survive into his 70s he may well have founded a better dynasty. After all, in retrospect, the early project of the Empire was to arrive at the Antonine era with its (albeit accidental) non-nepotistic "choose your own successor" model. Get there early and entrench it and you would have a very different time throughout the third century (No Aurelien though, which would be a shame).