The Robotech one is a lot more orchestral and sweeping, and the Macross one is kind of cheesy... but I do love the Firebomber cover of the Macross theme and the visual editing in that anthology video. 
I'd have to say on the whole though, that Macross's music is better than Robotechs (vocal music I mean!) Though some of the stuff from the New Generation isn't too bad... Minmay's songs are pretty terrible though >.<;;

EDIT: also, [url=http://www.youtube.com/watch?v=c1DbSdzFCsI&list=FLXHlSBT98kD_g0Ydhl4qawQ&index=2]the Shadow Chronicles version[/url] of the fanfare is pretty good too!