1.Nf3 vs 1.c4? What's the difference?

Well 1... e5 obviously.

"... it is also possible to reach many English lines, by starting out with the move 1 Nf3. The main advantage of this is that White avoids the whole complex of lines, starting 1 c4 e5. On the other hand, Black can reply 1...d5, which the English prevents. ..." - FM Steve Giddins (2011)

The English doesn't prevent 1..d5, and 1.Nf3 doesn't prevent 1...e5, at least not according to some of the patzers I've encountered.

Uninformed nonsense. Black plays 1.Nf3 if he rather plays the positions after 1.c4 e5 than those after 1.Nf3 d5 (or if he wants to have lines where the knight is developed on e2 in his repertoire, or if he wants to have lines where the knight development is delayed in his repertoire...).

I've played both, depending on what sort of position I want and if I know anything about my opponent's repetoire.

If your opponent plays 1...e5 exclusively against the English, 1. Nf3 is a good idea if your intent is to follow it up with 2. c4. Your main concern should be how 1. Nf3 meshes with the rest of your repetoire. For instance, what is your repetoire against the King's Indian Defense? It's hard to dodge the KID as an English player without making some serious concessions - if your repetoire against it involves an early Nf3, then you can play 1. Nf3 without any serious concerns.

1. Nf3 d5 isn't a huge concern for an English player - 1. c4 e6 (or ...c6) 2. Nf3 d5 is an instant transposition. You do have to be prepared for 1. Nf3 d5 2. c4 d4 or 2...dxc4. These, however, aren't terribly popular lines (perhaps unjustifiable so).

As summary, I would mostly base it with how often you place your knight on f3 in your English/queen pawn repetoire. If your knight always finds its way there anyways, 1. Nf3 has very few drawbacks and avoids a lot of Reversed Dragon theory.

C4 is explosive, Nf3 is not. 

Joder, Robert. Joder. That hurts.