Let us start with the Italian game.
Although it was long long ago since I was playing this opening, there are good reasons why it is not played anymore. The main reason it is not popular anymore is the failure of the Moeller attack*:
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4. c3 Nf6 5.d4 exd4 6.cxd4 Bb4 7.Nc3 Nxe4 8.O-O Bxc3 9.d5 Bf6 10.Re1 Ne7 11.Rxe4 d6 12.Bg5 Bxg5 13.Nxg5 h6 ( 13...O-O 14.Nxh7!= ) 14.Qe2 hxg5 15.Re1 Be6 16.dxe6 f6 17.Re3 c6
In the old days people played Moeller attack and in the beginning things were good for White-sacrifice a pawn and get strong initiative-but Black found a way to defend the attack-see the lines above-and the main line was destroyed. White tried with quiet
d3 and to prepapre
d4 like in the Spanish game ( Ruy Lopez ) but had no success.
People tried with Scotch gambit-mainly Max Lange Attack-but Black did not need much time to find antidote-that line failed White too so it was abandoned.
Same happened with Traxler attack and it was abandoned too.
Evans gambit had the same faith-I think Lasker was the one who proved that Black can at certain point return the pawn and obtain better chances due to better pawn structure.
Nowadays, people seek various ways to improve these old lines but nothing tangible was found-either Black can sidestep the improvements or they give equal play.
Now the good stuff-Ruy Lopez! After the moves:
1.e4 e5 2.Nf3 Nc6 3.Bb5
we reach the tabia. We notice that there is no symmetry like in the Italian game. Also, an important thing with Ruy Lopez is that White exerts MAXIMUM possible pressure on the center-that is the reason why it is better than Italian game, where center control is divided equally.
Because Black is under pressure he needs to make concessions, usually via
a6 and then
b5 to chase away the bishop-which leaves him with weak
c pawn. Because of advantage in the center and healthier pawn structure White has a long initiative and Black needs to play carefully to free himself. This usually manifests in White having a king side attack, or slight but long lasting positional pressure.
Furthermore, in Spanish game, White can create center formation he likes thanks to his flexible
d4+e4 pawn phalanx, something he can not do in the Italian game. This means that White can play with fixed center ( pawn
e5 ) , semi open center ( pawn
d6 ) or closed one (
e4+d5 pawns vs
d6+e5 ) and that gives him opportunity to try various transpositional tricks to outsmart Black-something that Italian game can not give you since the center is fixed and symmetric.
Ruy Lopez gives you a slight advantage in center, slight initiative, great flexibility in steering the game, healthier pawn structure and great transpositional resources to outsmart your opponent.
If you wish to improve as a player you should play this opening for a while, so you can learn how to play with different center formations and it is good for practicing how to "cash in" the king side attack.
Futhermore, in the Spanish does black have sharper continuations that he can throw against white?
Yes he does-the variation you seek is Marshall attack. It is very dangerous and being based on positional grounds i doubt a refutation of this gambit can be found-I think the current theoretical standing is unclear. Be warned, you must know theory very well to play against this line.
If you have further questions leave a comment and I will respond.
Sorry for incoherent answer, I wrote thoughts as they came to me. I could write a small book on this topic-there is so much to say about this-so if you need further information feel free to ask.
EDITED ON OPs REQUEST:
I am trying to understand if it is a lot better or only slightly better.
It is way better than Italian game.
Black defends statically in Ruy Lopez, there are no counter-attacks ( except Marshall attack of course ) so he needs to suffer a little in order to get counter-play.
Since you have ideal center-
d4+e4 pawn formation-you have slight space advantage. You also decide what type of game shall be played-open or closed-depending on your decision to close or open the center.
You get king-side attack and Black needs to defend himself-his counter-play on the queen-side is not sufficient. Be warned-Ruy Lopez is highly complicated to play for both sides but that is the reason people play it with both colors-because both sides must play accurate.
The reason I would not recommend it for Black is because Black lacks active counter-play so he needs to defend for a long time, before he generates chances and that is just too much for me.
Generally speaking, White has easier play in the Ruy Lopez, he "calls all the shots" most of the time and Black needs to repel White's threats first, and only then try to generate counter-play.
This is one of the main reasons why Black often answers to
1.e4 with Sicilian or French defense.
This was my opinion, supported by my current knowledge and experience in the Ruy Lopez and Italian game.
I must say that I have stopped playing
1.e4 long ago and that many things might have changed today but to test my claims it would be best to obtain good repertoire books on Ruy Lopez ( although I strongly believe that conclusions from those book will mainly support my conclusions ).
Hopefully this answer sheds some light.