Closed Ruy Lopez and Giuoco Piano (common Italian line) feel pretty similar to me as White. The Bishop eventually gets chased to c2. White develops and works to support a pawn push to d4. Both are pretty slow to get going.
For club players, the Italian is a lot more exciting. The Bishop on c4 aims at the vulnerable f7. If Black plays the Two Knights Defense, there can be a lot of fireworks. See the Fried Liver Attack, Lolli, and Wilkes-Barre/Traxler.
The ruy lopez is played twice as often as the italian game. Why? I don't see a big difference between e4 e5 Nf3 Nc6 Bc4 and e4 e5 Nf3 Nc6 Bb5 a6 Ba4 b5 Bb3. Yet clearly white must be better in the second line, because the ruy is much more common and black almost never plays 4... b5.
Why is the second position considered better than the first? The only differences are that in the ruy the pawns are on a6 and b5 and the white bishop is on the a4-d1 diagonal instead of the a6-f1 diagonal. How do these differences give white a better position?