So far as I know, no, there's nothing I can do as a CRI that you as a full FI can't do.
I can however, unlike an FI(R), work without direct supervision of an FI, and do biennial instructor flights. On the other hand the FI(R) gives the ability to teach ab-initio, which I can't do and an FI(R) has a much easier route to FI than I do, which for me basically means going back to scratch again regardless of my instructing hours.
G