Let me explain. We're going by both characters at their absolute best, right?
The Mother Elf is a program developed from X's Anti-Virus Program and Zero's Antibodies that was designed to end the Maverick Wars. After equipping himself with her, X reached the pinnacle of his power and single-handedly wiped out the Maverick Virus from the entire planet.
X didn't like holding so much power, so he unequipped her and had her stay in a sanctuary, where Weil (Dr. Wily 2.0) stole her and turned her into the Dark Elf to start another war.
The full extent of her power was seen in the third Mega Man Zero game, where she is linked with Omega, who is using Zero's original body since he got moved into a copy body and- (it's complicated).
Long story short, Zero beats Omega in single-combat and is about to finish him when the Dark Elf appears, blocking Zero's attack along with the subsequent attacks from the Guardians (basically X's kids who are all on the same level of power as him), albeit managing to injure Omega in the process and providing an opening for Zero to finally take him out.
In case you had a TL;DR moment, the Mother Elf is essentially X's last upgrade, a seperate entity that can restore him, amps his power, and can act seperately to shield him from the attacks of Four Large Star Level+ attackers at once.