I'm not that familiar with LIPA, but have just had a look at their undergraduate courses. A few comments:
1) At LIPA, it seems you'd be surrounded by performing arts students only - whereas at RHUL, you'd have a breadth of subjects spanning arts, humanities, social sciences, and sciences to make friends with. So it depends on what you'd prefer, socially
2) RHUL is closer to London than LIPA, yes, but I think with LIPA you'd actually be in Liverpool city? Whereas Egham (where RHUL is based) is a 45 minute train journey to London minimum, and that's once you get to the train station. Depending on how fast you walk, the journey from the Piggory gate or back gate of the main campus, to Egham station, can be up to a 20 min walk up/down a steep hill
3) At LIPA, you'd be studying more contemporary and popular genres of music. At RHUL, I believe you would have to study at least a few compulsory modules of Western classical music. So it depends how interested and confident you are in doing that