Eggyhead VS BossfightsX would be a victory for Eggyhead. Not really that crazy. Now that that's out of the way, let me explain.
X isn't weak. He has created an entire universe in his realm, and filled it with planets containing lifeforms of all kinds, however vile they may be. If the fight were in his own realm, he'd have an honest shot at winning due to his overwhelming power and control there. However, he doesn't really have a way to take Eggyhead there when they're in hand-to-hand combat. Still, he has the power to create and destroy universes and that is impressive. The thing is though, is that Eggyhead fights people on that level all the time. His whole job is to protect people from monstrous entities like X.
It's very similar to 2011X VS Sonic. It's not that X is weak, he's just dealing with someone whose raw power vastly outmatches him. Most of X's win conditions are countered by Eggyhead's abilities. Soul erasure? His soul is locked behind Wormwood under holy protection, which X can't really do anything about. Cheap shots and tricks? Eggyhead can either tank them or more realistically learn from them. Immortality? He can just be banished to the abyss where other spirits like him get sent through holy powers.
Like I said before, X, in any form or version, isn't a weak little critter. This isn't a hydrogen bomb VS a coughing baby, this is just a match-up that BossfightsX, or any version of X, is kind of countered by.
powerscaling grahhhh!!!!!!