After reading the two profiles, here's what I can tell:
Twilight's Mind manipulation won't work against The batter since he has resistance to it.
Her status effect inducement can get removed by The Batter's 2nd Add-on, Omega, by using it's competence, Frontal Perspective
The batter has healing and so does his add-ons, which is a huge advantage. Not only that, but he and his 2nd add-on both have resurrection.
The batter's add-ons have stats amps that can increase the batter's attack, defense, agility, and intelligence.
Twilight has causality manipulation and Bfr, but I'm gonna need more info about her causality and BFR powers
The batter has conceptual manipulation, but again, I need more information.
Both have Summoning, Light manipulation, Magic, some Reality Warping, Flight, and some other powers from his add-ons.
Result? Well, I'm kind of leaning on the batter because his add-ons have more haxes, but I'll wait until for people to respond and/or counter respond this.