Gregorius fights when necessary and mostly defensively. Most of it is building Traps and letting the Infrastructure do the Job instead.
Gregoriette fights if it looks like a fun thing to do. Mainly using weaponry that fits thematically to whatever she is fighting, so it’s not always a bullet hell.
Gregory will exterminate you efficiently if you annoy him too much. Typically by disintegration. To avoid friendly fire he may just use teleportation on you instead.
Edit: And yeah ofcourse there is a good and an evil side to all versions of me, though typically the evil side faces other evil things, which totally balances out to make good, right? XD