Ifrit is significantly more dps as long as you have a monk, even with proper use of contagion. This holds true for Turn 6/8/9, Garuda is closer on T7. I've only played with Ifrit since i103, so can't speak for anything less than that. The difference from then on though is very significant.
My question is, why does everyone think you have to start with and stick with 1 pet? I open with Garuda, Contagion my raging+pot+poison pot dots then swiftcast out to ifrit for the remainder of the fight. On T9 I can bring Garuda out for every Raging Strikes because of the fights downtime and not be affected mana wise.
For reference I can sustain ~415 dps on T8, where I use Ifrit the entire fight after I Contagion my opener. No poison pots. (i110 book)
Ifrit pulled 116 dps this week on Turn 9 - keep in mind T9 has A LOT of downtime, which makes that number much less than it would be on a 100% uptime fight. Find me a Garuda that can even get close to that. I also swap out to Garuda to Contagion every Raging Strikes which lowers Ifrits DPS as well.
Plain and simple - if you must use 1 pet for the entire fight, use Ifrit if you have a monk. Proper use of contagion on a fight like Turn 7 brings Garuda closer, and Garuda is better in situations where there is AOE and your dots will get to run their full Contagion duration. That leaves Ifrit by far better for T6/8/9.. if you have a monk. I highly suggest learning what your mana pool can handle though, and swap between pets accordingly for the best of both worlds. Usually only worth it on the opener, but in T9 there's plenty of downtime to hard-cast pets so you don't get stuck with Garuda out and no swiftcast after using Contagion.
As for the Mana concern, 1 short Ballad during T8 is enough to sustain ifrit - assuming the fight goes its full duration. T9 your mana should never be an issue. As I said I swap to Contagion every Raging Strikes, then swap back and can sustain myself for the entire fight. (Energy drain during golems)