F1 2013 is certainly not just an update. The addition of classic content is obviously the main new feature in the game, however there are also other bits that Codemasters have brought along or improved.
The AI is more aggressive, they feel more realistic. They are more intelligent, and different drivers have different strengths and weaknesses. For example Fernando Alonso or Lewis Hamilton are more likely to try and overtake you than Valtteri Bottas or Max Chilton.
Other than F1 classics, my favourite part of the new game is scenario mode. In F1 2012 it was very short and although quite fun, not particularly re-playable. Now there are far more sessions. It's not just trying to beat the champions either. It is now a little like a mini career, taking you through varying stages in someone's F1 life.
Back to the big thing though, F1 classics. I suggest buying the classic edition because it does add a lot more content (very good content). Each and every car handles slightly differently and you can play as some of the most iconic drivers of the 80s and 90s. Unfortunately Ayrton Senna doesn't make an appearance in the game due to licensing problems, however the drivers there are include Senna's great rival Alain Prost, as well as Nigel Mansell and Michael Schumacher.
Overall this is a brilliant game, and it will probably be the last Formula One game for current gen consoles so I sincerely recommend this game to anyone who has an interest in motor racing.