While I maintain, and frequently refer to, The Database - currently about 110,00 Jerome Gambit and related games - I occasionally like to drop in at lichess.org, an online playing site that has almost 6 billion games.
What are the simplest conclusions that I can draw from that massive collection of online club level play?
There are 804,880 games with the Jerome Gambit line 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+, with White scoring 49.5%.
Black does best to accept the Bishop with 4...Kxf7. The lichess.org database has 783,491 games with that move (the overwhelming choice), with White scoring 49.5%.
Instead, against declining the piece with 4...Kf8, seen in 18,867 games, White scores 58.5%.
Against the other declination, 4...Ke7 - 2,522 games - White scores 64%.
After Black takes the piece with 4...Kxf7, White has seven main continuations.
Most frequently played is the thematic 5.Nxe5+, appearing in 506,616 games, with White scoring 52%.
It is interesting to note that 5.c3, while appearing in only 62,659 games, scores a bit better than that for White, at 53%.
Next in success for White is 5.O-O, appearing in 67,291 games and delivering 49%.
That is followed by 5.d4 (85,870 games, White scores 47%), 5.d3 (39,832 games, White scores 43%), and 5.Nc3 (6,771 games, White scores 41.5 %).
The notorious "Face Palm" variation, 5.Ng5+ appears in 35,765 games and scores 31%.
For comparison, the main line of the Giuoco Piano, 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.c3, appears in 22,953,410 games in the lichess.org database, with White scoring 54%. That is clearly better (but not by a lot) than the Jerome Gambit accepted, but not as good as the Jerome Gambit declined lines.
[For a similar, 14 1/2-years-earlier look at Jerome Gambit lines, check out "A Closer Look at the Big Picture (Parts 1, 2 and 3)" which noted "Likely what is needed some time in the future is a Closer Closer Look at the Big Picture.".]