I have both books now. MRQ is my preference mainly because its the sanctioned system for Elric and Hawkmoon (just picked up the latter the other day along with the GM screen, which is very nice). From the looks of it, aside from completing the Elric/Hawkmoon collection, I may have to pick up Glorantha:2nd Age (at least) as well as Lankhmar and Slaine. The various types of powers in the rules are appealing, and I like the combat rules.
BRP is another monster altogether. After reading through it, it seems to remind me a bit of True20, inasmuch as its a toolkit rather than a game in itself. Not that this is bad, considering I have all the True20 books on since Blue Rose. Yeah, BRP does come across as a nifty set of tools that can be used to enhance MRQ. In fact, I would consider using BRP alone if not for the aforementioned Moorcockian games. Rules I may implement include the Strike Rank rules (where number of attacks is determined by SR), some of the powers rules, and pretty much what strikes my fancy.
Side by side, things aren't much different. Weapons and armor seem a touch more powerful (as in a +1 here and a +2 there) than in MRQ - which makes crossover easier. I love the list of professions in BRP, which can really help flesh out a multiversal campaign. From MRQ, I am growing fond of Hero (Fate in Hawkmoon) points and Legendary Abilities. All in all, now that I have both books I can't honestly see running a game without both handy.