Human Jaeger - Claymore
Salarian Jaeger - Rapier
Turian Jaeger - Katana
Asari Jaeger - Morningstar
Krogan Jaeger - Battleaxe
Elcor Jaeger - Shield
Hanar Jaeger - Harpoon
Batarian Jaeger - Whip
Humans are a lot more adaptable than most species, Jaeger-wise. They had everything from the Russian Tank (who survived as a MARK I all the friggin way to the Double Event) to the Speedster (Striker. though, granted, as a MK-V he had strength too, but mainly speed), and the Swiss Army Robot (Gipsy. No matter what it goes against it WILL have a weapon to say fuck you with.). I think this isn't
just because they were the first species with Jaegers, but more because unlike the rest of the Citadel and etc species, their bodytype is more adaptable and varied.
You've got balloon-Volus, elephantine Elcor, jellyfish Hanar, Lizard-Bird Turians, and so on. A lot of the species are visibly adapted for animal-to-animal combat, something that doesn't exactly scale up very well with giant robots. Physically they have a lot less variation than humans. I've never seen or heard of obese Turians, muscle-bound Asari, or anything less than the perfection of physical strength Krogan. Humans on the other hand have brutes that can be similar to Krogan, tactical hit-and-runners like Turians (I don't believe their pre-tech ancestors hunted with prolonged fighting in mind), and so on.
Salarians would probably have a focus on using speed and gadgets. Gipsy Danger style maybe. Get in there, hit it with some kind of Tesla-Spike that periodically discharges enough voltage to completely fuck up its nervous system, and then slice and dice for the kill. Most likely they'll be running support Jaegers, if at all.
Turian Jaegers I expect to actually be
smaller than standard. The neural load for the massive Jaegers was only doable with two heavily
synchronous minds acting in unison. If their Jaegers were smaller (though not by too much, mind you,) the load required would be a tad smaller and make it theoretically easier to find Drift partners (ironically I think the Turians are going to be the easiest to find partners for since
every single one of them goes through service. Just find two old buddies who went through the same tours and lived vaguely similar lives post-service (if they left) and you're probably set). With smaller Jaegers, they could field more and work as a cohesive unit to
swarm the Kaiju, which would be an interesting and most definitely Turian tactic. And then we give them all mortars like Coyote Tango!
Asari... outside of heavy biotic artillery I expect their Jaegers to be effective purely through the amount of money thrown into their construction. The Asari aren't a very physical-combat inclined race, like the Humans (yes I saw that HFY tumblr pic a few pages back but we're tactics inclined, like Turians), and use guns and biotics to get by whenever there's trouble they cant talk their way out of. The former is uneffective at Kaiju size, and the latter is probably more expensive and dangerous than its worth using it.
However, that being said, they do have a
very long lifespan and can make up for their seeming physical weakness with a heavily power-up Jaeger and centuries of hand-to-hand combat training. They probably trump half the other species due to sheer skill, when they put their minds to it. Similarly, their extremely long lives would make finding a partner awkward, if not outright difficult, and probably very prone to chasing rabbits.
And I got bored about here and will probably finish my extensive overthinking of species to giant robot comparisons/thoughts later.
Krogan Jaeger - Battleaxe
Elcor Jaeger - Shield
Hanar Jaeger - Harpoon
Batarian Jaeger - Whip
(And yes I forgot to read the rest of the post I got the quote from so I probably completely missed the point but GOOD MORNINGGGG)