Robb and Jon are both 17 at the start of the show. This is in contrast to the books where they are both 14 at the start.
As to who is older, I don't think there is a Canon answer to this. The closest I'm aware of is this book quote implying that Robb is older.
Many men fathered bastards. Catelyn had grown up with that knowledge. It came as no surprise to her, in the first year of her marriage, to learn that Ned had fathered a child on some girl chance met on campaign. He had a man’s needs, after all, and they had spent that year apart, Ned off at war in the south while she remained safe in her father’s castle at Riverrun. Her thoughts were more of Robb, the infant at her breast, than of the husband she scarcely knew. He was welcome to whatever solace he might find between battles.
I read this to say that Robb was conceived before Ned went off to war, while Jon was conceived during the war. (Obviously assuming that Catelyn's understanding of the situation is correct)
Adding detail related to the above quote to reflect Season 6.
In season 6, we discover that Jon Snow is not Ned's son after all, but rather the son of his sister (Lyanna Stark) and Rhaegar Targaryen. This is in contradiction to Catelyn's understanding of the situation and so invalidates the quote above as a legitimate source for this answer.
Due to this, the best that can be said at this point is that Robb and Jon are very close in age.