I don't think the Leafs think they are better than what they are to be fair as shown by the level of the rebuild thats just started, and its also hard to argue with the fact that it is the biggest team in hockey.
But anyway a few bits regarding Stamkos...
1) Plays for his home town/boyhood team and becomes the face of the franchise and the rebuild (will only be 26 when he becomes a FA)
2) Big salary available and opportunity to make a lot more in endorsements in Toronto than he can in TB (if moneys a big factor)
3) Gets to play centre rather than on the wing where TB seems to want him to play
4) Opportunity to work under one of the best coaches in the game in Babcock
5) Guys like Nylander and Marner coming through in the next year or so
He might very well end up staying in TB (who are going to have to give out big money to a number of players in the next few seasons), but I think that its daft to say that there isn't an attractive proposition for him in joining the Leafs.