Farms > Jungle for science...
... no?
Farms are +3 food; +4 after fertilizer (off the tech path).
Jungles are +2 food, +2 science, +1 gold; +2 food, +3 science, +2 gold after economics and rationalism (both of which you are going to get very quickly).
After schools, each population = 2 science. So, EACH farm has to be responsible for 1.5+ pop for the tradeoff to be worth it in strict science terms (the extra 1.5 pop'll get you ~3 food/hammer, but costs 1.5 happiness; the jungle gets you +2 gold). The problem is, you're never getting 1.5 extra pop. And before you reach 1.5 extra pop, the 2-science tile continues to win, for all those turns (which, as you'll see below, is all of the turns in the game). In fact, the effects of getting the science earlier, so you can hit science-buildings earlier probably snowball into greater benefits, but we won't go there.
By an endgame of 35 pop (conservatively), it's 800 food per pop. So, you need 1200 food to break even. On that extra +2 food, that's 600 turns (~450 turns w/ aqueducts). You may be able to cut that turn time down with Tradition or other growth modifiers, but you'll never get down to the ~120 turns left in the game by the time you hit rationalism/economics/fertilizer to make up the difference (or the ~180 turns by the time you hit civil service/education).
This is all not to mention that you're trading 1 food for 2 science on all non-riverside tiles for a good chunk of the game (and if 2 food for 2 science doesn't work to the farm's favor, I don't have to show you the math for 1 food 2 science).
Now, the balance is how fast your cities are growing. If you end the game with 20 pop city, it'll only take 500 food to get to the next pop, and farms would in all likelihood be better than jungle tiles.
So, the best way to treat a jungle city, is as you might expect, is to send ITRs once you have a happiness bubble to pump food while saving jungle. If you're really running out of tiles to work in the early game, chop the riverside ones, but keep the rest in tact. If you don't have ITRs to spare, because this is your 4th city or w/e, and you don't expect this city to every grow beyond 20pop, and there's not enough farmable land around... (first, why the hell did you plant this city in the first place?)... and you have zero happiness issues... then cut jungles as needed to farm. I never cut non-river jungles that don't have another resource.
On the other hand, if your cities are going to stay small, with a lot of time left on the clock, and you have no happiness issues, and you're going to build science buildings at least through schools, then go for farms, and by that, I mean avoid the damn jungle to begin with. This happens very rarely. You'd have to conquer an AI city at the exactly right period (after their cities are large enough that you wouldn't raze, but before the time when they've cleared the jungles...).