Well, I can tell you you put them in order.
Roads add 1 commerce (which you don't notice but adds up, unless the city is totally corrupt) and of course the link your cities and get you resources. They shouldn't even be on the poll, it should just say "Mines vs. Irrigation".
I'd say Mines if that was the case. Although food is important early in the game, shields in my opinion are more important than food later in the game. Seeing as how food is going to expand your jungle cities and cause disease and a bunch of problems, I'd rather have a small city adding every little thing to my massive Empire. I mean, jungle cities are usually built for the Luxury Resource found nearby anyways (in this case, Silk(?)). You still need food though, I just value mines higher. Remember, Irrigate Brown, Mine Green. As long as all your squares have at least 2 food, you're good to go.
PS: I accidentally picked Mines because I didn't think roads would be on this Poll. I thought it said Rails at first glance. Although I do like moving anywhere in my Empire in 0 turns.