I disagree with your comment that 3.e3 is simply better for White - after 3...e5 4.Bc4 ed4 5.ed4 Nf6 6.Nf3 Bd6 7.0-0 0-0 8.Nc3 Nc6 or 8...h6, I don't see why Black is any worse.

My comment was that 3. e3 is better for White if Black tries to hold onto the c4 pawn, not necessarily in all variations.

I had never seen the 3. ...e5 line of yours before. 3. ...c5 also gives Black a perfectly fine game, as he/she will have a target to aim at in White's isolated d4 pawn.

Indeed. However, whilst 3...c5 is perfectly playable, White seems to obtain excellent compensation for the pawn after 4.Nf3 cd4 5.Bc4 Qc7 6.Bb3!? de3 7.Be3 with a large lead in development for the pawn. In practice White's results are very good.

Black can also try to hang on to the pawn with 3...Be6, but then simply 4.Nf3 Nf6 (4...c6 is somewhat better, transposing to the Slav) 5.Ng5 favours White.