This question seems to come up quite often. It's not long ago when there was a similar thread.
Now, I am not going to say that Ruy is better than Italian or vice versa. However, it seems that many people are worried about the fact that black can chase white's bishop around in the Ruy. There's no need for this. Compare this Italian position
to this position from Ruy Lopez
The positions are very similar (white's king bishop is on the same diagonal). In the Ruy black has gotten in the extra moves a6+b5 so does this mean he stands better? No, it doesn't! This particular Ruy Lopez position is almost certainly better for white than the standard Italian position. Only possible bonus for black is that in some cases he might be able to develop his bishop to b7. On the other hand b5 might also turn out to be a weakness: white can later play a4 when he gains possibility to open the a-file and attack the weak b5 pawn. Most important difference favouring white is however the fact that the bishop is much more stable in b3 than in c4. In particular white doesn't have to worry about blacks d5-break anymore. Please compare the variations above to see how important this d5-resource is in the Italian.
Where I come from your first diagramed moves are not from the Italian game, but from the "two knights defense". I think, if my memory serves me well, your line leads to something called the "Max lange attack"
Chess.com:
chess365.com:
So as you can see, there's really not much in it (even at Master level).
Personally, I play 2. f4 about five from six and 2. Nf3 Nc6 3. Bc4 for the remainder. My reasons are simple, I don't play chess to manoeuvre for 25 moves to win a square or gain some minor concession. I like to smash holes in the opposition or die trying. I am completely unabashed by short losses and enjoy the extra time at the bar or watching my club-mates sweating over tight games.