In the top diagram, white is better because he will probably regain the piece and blacks king is in the center...
I refuted the Italian game, so I don't play it ... [5. ... Na5] is winning for Black [after 1. e4 e4 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 5. exd5] ...
"... [5...Na5, 5...Nd4, and 5...b5] have been developed to try to justify Black's opening play. ... whether these lines really offer full compensation for the missing pawn is as unclear today as it was one or two hundred years ago. ..." - GM Paul van der Sterren (2009)
The March 2017 issue of Chess lists the top twenty openings compiled from a list of 1795 January games where both players were rated over 2400 Elo. One can not take position on this list too seriously because it is greatly influenced by how the openings are grouped. For example, all the Retis are grouped together, while English is separated into 1...c5, 1...e5, etc. Nevertheless, for what it is worth, some of the list entries are: 107 Retis, 89 Caro-Kanns, 87 King's Indians, 72 Najdorf Sicilians, 71 Nimzo-Indians, 65 Slavs, 46 1...c5 Englishes, 44 Classical Gruenfelds, 42 Queen's Indians, 40 1...Nf6 Englishes, 39 Taimanov Sicilians, 37 declined Queen's Gambits, 36 Kan Sicilians, 31 1...e6 Englishes, 31 Italians, 31 Semi-Slavs, and 28 Catalans
A number of recent books have advocated the Italian game for White:
A SIMPLE CHESS OPENING REPERTOIRE FOR WHITE by Sam Collins
http://www.gambitbooks.com/pdfs/A_Simple_Chess_Opening_Repertoire_for_White.pdf
My First Chess Opening Repertoire for White by Vincent Moret
https://www.newinchess.com/Shop/Images/Pdfs/9033.pdf
Winning with the Slow (but Venomous!) Italian by Karsten Müller and Georgios Souleidis
https://www.newinchess.com/Shop/Images/Pdfs/9037.pdf
I refuted the Italian game, so I don't play it