From what I have seen in the database, Bc5 (19,000+ games) isn't significantly more popular than Nf6 (16,000+ games).
I think all your points are perfectly valid - There usually isn't a huge difference. But apart from what you mentioned, if Black plays Bc5, he needs to learn how to deal with b4 as well.
Both are fine if you know what you're doing but after 3...Nf6 you get 4.Ng5 which is fine if you know what you're doing but people probably don't like playing against it in the Italian.
It's probably because 3...Bc5 gives black the best chance to win with the least amount of risk taken.
From what I have seen in the database, Bc5 (19,000+ games) isn't significantly more popular than Nf6 (16,000+ games).
I think all your points are perfectly valid - There usually isn't a huge difference. But apart from what you mentioned, if Black plays Bc5, he needs to learn how to deal with b4 as well.
This is probably it; ...Bc5 requires study into b4 lines as well. Personally, I have played both. I used to play 3...Bc5 but since switched over to playing 3...Nf6 versus the Italian. The b4 lines had nothing to do with it though. In fact, I loved facing the Evan's Gambit because I liked the theoretical mainlines 
That was actually something I missed by not playing 3...Bc5 in my repertoire.
I switched to The Two Knights versus the Italian Game (3...Nf6) because of transpositional considerations.
As noted, both moves ...Nf6 and ...Bc5 are certainly fine to play though - just a matter of preference, style and taste (as well as how much study and which mainlines you want to embark on).
One risky plan is the Traxler
raxler
Yes the traxler is interesting, but white can get an advantage with 5. Bxf7. In 3... Nf6 4. Ng5 , I know blacks best line is 4... d5 5. exd5 Na5. But there is some advantage to playing 3... Nf6 since after 3... Bc5, white can try 4. d3 Nf6 5. d4 exd4 6. e5, which is a serious try. I guess the reasoning behind 3... Bc5 being more popular than 3... Nf6 is that most players rather face the c3 d4 line over the 4. Ng5 line. But I don't think that there is a problem in the 4. Ng5 line.
5. Bxf7 has a slight advantage, yet the position is drawn. 5. d4! is the best, with 5...d5.
5. Bxf7 has a slight advantage, yet the position is drawn. 5. d4! is the best, with 5...d5.
Are you saying 5. d4 after 4... Bc5?
I realised I hadn't finished the above and edited it. Before the edit it didn't make sense. Hope it does now.
Not playing Nf6 won't be anything to do with 4. Ng5, which isn't very good and at best may give white a very small plus. The Traxler loses outright for black. I only had it played against me about twice.
There are two lines that draw, and one where black is a pawn down (out of three).
5. Bxf7 has a slight advantage, yet the position is drawn. 5. d4! is the best, with 5...d5.
The best is Nxf7
yes.
No, it's 5. d4! Look at this forum if you don't belive me: https://www.chess.com/forum/view/chess-openings/whats-the-best-way-to-counter-traxler-counter-attack
I think the main question in 3... Bc5 vs 3... Nf6 is comparing these 2 lines:
I think that these 2 lines are the most critical test for black in the Italian (besides the main line) and the main factor in deciding what to play on the 3rd move. I'm just surprised that in recent super gm games, 3... Bc5 is being played way more often then 3... Nf6. I'm not sure why, but if I had to guess I would say that top players think that 4. Ng5 is harder to deal with then 4.c3 5.d4. Personally, I think that the 2 lines are very close in terms of challengingness, that's why I'm surprised that one of the moves is being played much more frequently then the other, at least according to my database.
I think the main question in 3... Bc5 vs 3... Nf6 is comparing these 2 lines:
I think that these 2 lines are the most critical test for black in the Italian (besides the main line) and the main factor in deciding what to play on the 3rd move. I'm just surprised that in recent super gm games, 3... Bc5 is being played way more often then 3... Nf6. I'm not sure why, but if I had to guess I would say that top players think that 4. Ng5 is harder to deal with then 4.c3 5.d4. Personally, I think that the 2 lines are very close in terms of challengingness, that's why I'm surprised that one of the moves is being played much more frequently then the other, at least according to my database.
I think it's mainly a practical choice.
In correspondence chess Nf6 is more popular than Bc5, that shows that objectively the line is not all that dangerous for Black.
But Nf6 Ng5 requires a lot of additional preparation, they already have to prepare enough other stuff like 1. d4, Ruy Lopez. So why bother with another line, that requires a lot of work but is unlikely to happen because most White player will play 4. d3 anyway.
And the positions after Nf6 Ng5 are much more double edged, while super GMs usually prefer being solid and make a draw with Black. If they want a sharp game, they don't play 1... e5.
Hello, I've been looking at the recent high level games (2700+) and realised that 3... Bc5 was significantly more popular then 3... Nf6 in the Italian. To me, both moves seem to be of equal strength, they just give white differant extra options. I think the main difference between the 2 move order is that against 3... Nf6 white has the extra option of playing 4. Ng5, while against 3... Bc5 white can play 4. c3 Nf6 5. d4. So do the top players think that this Ng5 line is worst/more work then this c3 d4 line, or am I missing something. As far as I know, both lines are perfectly fine for black, yet 3... Bc5 is played like 5 times more in super gm games.