After the second option 1.c4, White can increase pressure on d5 by Nc3/g3+Bg2/Qb3/e4 etc. Black can fight for d5 with pawns by first playing 1...e6 or 1...c6 (heading for a Slav Defence after 2.d4 d5). The weakness of 1.c4 is that it does not counter other central squares available for Black's focus, such as c5, d4, e5, and e4. Black can play 1...c5, 1...e5, 1...Nf6 or 1...f5 (Dutch Defence). Sometimes I also play 1...Nc6 intending 2...e5, 2...d5 or 2...Nf6 depending on what White chooses and what Black prefers.
Some books on the English Opening hardly mention 1.c4 d5!? at all. The obvious positive plus about this line is that if Black already knows a line after 2.d4, then does not have to learn much that is unique to the English Opening after 1.c4. It is common for such books to be a summary of how top players handle the opening. Top players rarely play 1.c4 d5. Chess database game collections are heavily weighted by grandmaster and master games. Club players make it into databases much less often.
The average rating for players in my large database with millions of games is about 2300. The rating for players as Black in the opening 1.c4 d5 is in the 1900s and occurs about one out of every 300 games. In my experience as White after 1.c4 I faced 1...d5 once every 20 games; the average player who played 1.c4 d5 vs me was rated in the 1600s. Compare that to the most common move that I have faced from Black after 1.c4 which is 1...Nf6 (over 200 times) where Black was rated on average 2109.
This MaryDawson vs Sawyer game saw me play my prepared line after 1.c4 d5 2.cxd5 Qxd5 3.Nc3 Qd6! 4.Nf3 e5. Clearly White has a lead in development, but Black is not dead. There are good chances for Black to complete his development. For the fun of it, in the notes, I have added a simultaneous exhibition game where the world champion Emanuel Lasker lost to an unknown opponent in this line 100 years ago.
My English Tactics book (1.c4) has 500 combinations and checkmates.
My Checkmate Tactics book has the best 500 opening mates.My Combination Tactics book has the best 500 ways to win material.
5.g3 a6 6.Bg2 Nf6 7.d3 Be7 8.0–0 0–0 9.Bg5 Nc6 10.Bxf6 Bxf6 11.Ne4 Qd8 [11...Qe6=] 12.Nxf6+ Qxf6 13.a3 Be6 14.Rc1 Bd5 15.b4 Rac8 16.Qd2 Rfd8 17.Rfd1 Nd4 18.Nxd4 exd4 19.Bh3 Be6 20.Bg2 Bd5 21.f3 Bb3 22.Re1 b5 23.Rc5 c6 24.Qc1 Bd5 25.h4 g6 26.Kh2 Qd6 27.e4 dxe3 28.Rxe3 Re8 29.Qe1 Kf8 30.Rxe8+ Rxe8 31.Qc3 [31.Qd2 Qe5=+] 31...Qe5 [31...Re2!-+] 32.d4 Qe3 33.Qxe3 Rxe3 34.g4 Rxa3 35.Kg3 Rb3 36.h5 Rxb4 37.hxg6 hxg6 38.f4 Rc4 [38...Rb3+ 39.Kf2 Rb2+ 40.Ke3 Rxg2-+] 39.Bxd5 [39.Rxc4 Bxc4-+] 39...Rxc5 40.dxc5 [40.Be4 Rc3+ 41.Kf2 b4-+] 40...cxd5 41.Kf3 a5 42.Ke3 a4 43.Kd3 a3 44.Kc2 b4 45.Kb3 Ke7 46.f5 gxf5 47.gxf5 Kd7 48.f6 Kc6 49.Kxb4 a2 50.Kb3 a1Q 51.Kc2 Qa3 52.Kd2 Kxc5 [White resigns] 0–1