I don't think the protocols are very efficient in general - it depends on which RNA pool you are looking at and abundance of the proteins you are interested in. The cross-linking is reasonably efficient, but there are limitations in how much (RNA or protein) you can detect and how good your fragmentation protocols are. I would expect substantial losses at most stages of these protocols. I have heard of people refining these sorts of experiments to work on limited size clinical samples. RNA pull downs of polyA-mRNA are reasonably good these days, but will have carry-over of non-polyA mRNA. The best kits for this are not at all cheap and you can expect to use them rapidly as you need to start with large amounts of RNA.
Note that CLIP protocols are usually targeting detection of RNA species for binding of things like transcription factors to particular sequences. You will need to adapt for detecting proteins - talk to your mass spec people about this.
However, with the advent of mass spec techniques, it has become more feasible to do these sorts of experiments and get some meaningful data out.
I would go with a generic protocol and refine from there. In most downstream situations you will have specific questions that you want answered, and without the specifics you can't easily use a refined protocol for these.