I have heard the Rockports (Mira, Ankaa, Acquila, and Altairs). I have also heard Monitor Audio speakers in the $6K range (forget the model now) and just comparing house sounds, I much prefer Rockports. Rockports sound natural, tonally dense and like real music but with all the resoluton and dimensionality that typify high-end audio speakers. The Monitor Audio speakers sounded like hi-fi speakers to me, tipped up in the treble region, somewhat analytical, a little thin in terms of tonal balance, although plenty of bass. So I admit, I have not heard the MAs in question and I am a big fan of Rockport speakers and Andy Payor, their designeer, but I am giving you my best guess.
I totally agree with Ricred1 that there is no substitute for listening for yourself and making your own mind up. We can give you our opinions but we all have different priorities in what we look for in a speaker and your tastes/preferences are the only ones that matter. Plus, you should make sure that whichever speaker you choose will play nice with your audio gear, so that is another reason why you should try to audition these speakers ideally at home with your gear or at a dealer with gear that most closely approximates what you have at home.
Whatever you decide, good luck and enjoy. Researching and auditioning gear is always fun.
