For the JSA vs X-Men (note: I don't know what all of the JSA's powers are)
Flash vs. Cannonball: Tough choice, but Flash is faster and probably has the experience.
Starman vs. Havok: Don't know, maybe Starman.
Power Girl vs. Rogue: Rogue distracts with flames, then moves in for the touching. I'll call this the wet-dream fight.
Hourman vs. Colossus: Don't know.
Damage vs. Warpath: Warpath is viscious if he needs to be, he's got it.
Green Lantern vs. Cyclops: Sorry Cyke, if Tony couldn't, you can't.
Obsidian vs. Nightcrawler: Don't know what Obsidian can do.
Mr. Terrific vs. The Beast: Terrific has a tech edge, but Beast has the experience and animal instincts, this could go either way really.
Liberty Belle vs. Emma Frost: Emma, unless LB can guard against psychic and diamond fist attacks.
Cyclone vs. Polaris: Experience wins it.
Stargirl vs. Marvel Girl: Marvel Girl, no contest.
Hawkman vs. Sabretooth: Sabertooth eats this canary for lunch.
Wildcat vs. Wolverine: Wolverine is bester at what he does.
Jakeem Thunder vs. Darwin: No idea.
Dr. Mid-Nite vs. Mystique: No idea.
Sand vs. Iceman: Iceman can just freeze him.
Commander Steel vs. Cable: Don't know.
Mr. America vs. Shadowcat: Shadowcat does have extensive ninja training, and you can't touch her.
Well even though some fights are undecided, the X-Men are the clear winners here.