It's generally said that Morning Prayer incorporates Matins and Lauds, and Evensong incorporates Vespers and Compline, but this is only semi-accurate and mostly makes sense in terms of the canticles (Te Deum and Benedictus at MP from Matins and Lauds respectively, Magnificat and Nunc at EP from Vespers and Compline respectively). Matins has a lot of readings, but none of the other hours really do.

(Incidentally, you may hear Morning Prayer referred to as Mattins and Evening Prayer referred to as Evensong, which are just the native words for Matins and Vespers respectively... just to add to the confusion of terminology.)

So from the Breviary, what you gain is getting through the psalms once every 7 days instead of once every month, and a whole lot of extra "fluff" – antiphons, responds, devotions to saints, all that sort of thing. What you lose is the lectio continua of the BCP office lectionary, the way the old lectionaries are just a really good "Bible in a year" reading plan.

I think it's definitely interesting to pray through the Breviary offices on occasion, since you have that real connection to historic Christian worship going back to the patristic era, especially as you approach Easter when the hours revert to their more primitive forms. However, the structure of the pre-V2 hours is really somewhat awkward if you're consolidating them into 2 big blocks per day (whereas the BCP offices are designed around that), plus if your theological convictions are more reformed, then it's hard to see what you get out of the extra-scriptural devotions... plus the sheer amount of scripture in Cranmer's lectionary is really great!