Aah, I'm stupid. Disregard me then.
Well, first thing I noticed, right off the bat, is that The Batter's got Solar System level AP and Dura, to Mega Man X's Large Star+ (1787.6 FoE vs 3.52 FoE), so already he's going to have a considerably harder time taking down The Batter than vice versa in a contest of raw power. Speed's a moot point, so disregarding that.
Now, as for other stats/abilities...
Intelligence: About the same.
Stamina: Limitless for all intents and purposes.
Range: X seems to have a slight edge all things considered but it's likely not going to matter all that much given their speed, and that their maximums appear to be about the same.
Lifting Strength: Also goes to X by a little bit... will this even come up?
The Batter vs Megaman X
Stealth: Countered by invisibility, and both can perceive on another still so moot point.0
Healing: Countered by X's (rather high) regen.
Resurrection: X also has it.
Flight, Elemental Manipulation, Light Manipulation, Reality Warping on a Planetary Scale, Hand-to-Hand Skill: Both have them.
X has got mind/soul manipulation as well as transmutation, and The Batter can resist it, but to what degree is unknown.
The Batter can existence-wipe (hence why he's able to kill X at all), and X can resist it, but to what degree is unknown. It would also warp the landscape to better suit The Batter, only for it to be replaced by a new battleground/weather by X as that's something he can do, which would basically just put the planet in a state of permanent flux.
The Batter has his Add-Ons, which basically means there's four of him: the question is, can X's duplicates actually attack and take hits, or are they just basically Shadow Clones/fakes?
X can become invulnerable, and that's a godsend in terms of a fight like this. Thing is, does it have a time limit? If so, The Batter would probably find out in short order and run away until it expired, he did the exact same thing against Enoch.
X also has Time Manipulation, which can probably help him escape attacks and land lots of free hits.
The Batter can inflict and cure a whole ton of different ailments, I'd imagine some would dramatically hamper X's ability to fight well. Im Impossible Embrace lands and X gets Palsied, it's basically over, and he can also boost his own stats with Epsilon. Their gigantic array of items will further keep them raring to go as long as they need.
As far as weaknesses... The Batter doesn't really have anything that would come into play here, as no player is controlling him now and his pride doesn't cause him to hold back. X, I guess you could argue that The Batter would use his Fourth Wall Awareness to take a look at X's profile page here on this site (no really, that's literally something he can do), but A: it's possible that he needs the Puppeteer's (player's) help to do so, and B: He probably wouldn't use the information anyways, that would be rather Out-Of-Character.
...all in all, still slightly inclined to give it to The Batter due to the DC/Dura disparaty and the fact that X would have a hard time keeping up with four enemies with speed equal to his at the same time, especially with the stat boost's running about and such. I'm not entirely sure though, from the looks of things this is one of those fights that could for all intents and purposes go on forever.