It sounds like the hooks you are using are match carp hooks although i may be wrong. If thats the case just buy some hooks aimed at carp fishing like Korda wide gapes or ESP Raptors.
Depends on the method im fishing, what bottom im fishing over, how the fish are feeding ect ect so i cant answer because i use all 3 for different situations.
Im totally confident in the hooks im normally using i just liked the look of muggas and was going to have a play around with a rig on the 2nd rod to see if i could maximise my catch rate as ive heard the mugga has a good hookhold.
Is it because of the shape of them they can penetrate deeper?