Just make Ifrit autoattacks give mana back to the caster.

Alternatively, make all of Ifrits autoattacks splash.

Alternatively, make burning shield just an immolation aura instead.

The point is to make the different pets be useful in different situations.

The goal of every pet is "more dps" so regardless of what you do, if all you focus on is "more dps" people will just use that pet.

If you make ifrit do double garuda's damage, people will just use ifrit. That doesn't solve anything.

Better to give them niches. Ifrit for extended engagements, and/or AoE, garuda for single target.

This is how everything works, because of min maxing there will always be exactly one answer for optimal dps on every single situation.

If you want more (or rather, any) of those situations to favor ifrit, you need to be careful not to make it crowd out garuda.

I mean it doesn't even matter what their names are. Its Summon A vs Summon B. THey are "interchangeable" in that if you buff one and its better than the other, it'll just replace it.

So again, niches please, rather than straight up damage increases.

And frankly, don't even care about it. Use ifrit if you want. You'll still be able to kill everything you've been able to before, unless you are on the bleeding edge of being able to down a boss.