A fight between an Ekaide and and Eisenhower? Interesting question. Probably a bigger can of worms than you want to open though. Bigger than anyone wants to deal with really. But if you're certain...
First of all, they're both adaptable with fully functional hands. So we have to ask - what are they bringing to the party? An Anti-Tank Guided Missile will flat out vaporize the alien suit, if it locks on and tracks. Fifty-cal rifle - you might, might put holes in it - up close. A standard infantry level machine gun, and you're just scuffing the paint job. Flipping this around - ceramics in the Ike's armor give it some measure of damage reduction against lasers, but radiation cannons - hiding behind a wall won't help.
How about terrain? Ekaide are larger, faster, and yet still surprisingly nimble. The Ike is less than half its size so it can hide and ambush better. I can't say much about the alien's sensor package, but I'd guess they would hold the field in open terrain, and the human rules the city. Of course, that spoils it a bit since Humans always have the home-field advantage if we make it an urban fight.
Time is also a factor. Sure, the Eisenhower can sustain combat operations for between two and three days, and the batteries last longer yet in low-power mode. The Pilot? Less so. An Incubus is more of a robot, so the alien inside is sitting comfortably and pushing buttons. Would it like being cooped up for a few days? Doubt it, but they've probably got an autopilot and air-conditioning that actually works.
Training is going to be the biggest factor, and also the one I can say the least about. I can't say much about how a Citizen drills, or if they have the resources to train much. Most human groups probably don't. If you've got a former user from the war, and give them some time to refresh, its good. The average scavenger teaching them-self to use a suit - more luck than anything.
My money would be on the alien, if that means anything.