I've seen most of the Macross franchise, and a smattering of Gundam (mainly the U.C. stuff -- 0079, 0080, 0083, Zeta, F91, Char's Counterattack, V Gundam). There are a lot of good things about both franchises, and both have a lot of pretty epic moments. If I had to choose, though, I'd go with Macross.
Original Macross / Robotech rewrite - great story, iconic mecha designs, good character designs. IMO, the original Macross music lacked the dramatic punch that the Robotech music had, but overall a true classic.
Macr 7 - I so wanted to hate this show when I first watched it, but it is just all flavors of awesome. Everything about it is so ridiculous that I couldn't help but love it. If the music wasn't upbeat rock, I probably wouldn't have liked this one half as much.
Macr Zero - I dug this one even though my roommate hated it...
Macr Plus - Great show, but it's been 10 years since I've seen it, so I barely remember it.
Macr Frontier - The end of the 1st episode really grabbed me. Almost everything about this show really impressed me -- the animation style, the music, the mecha, the characters.
On the Gundam side, 0083 is the OVA I like to show new anime fans as an intro. Kou may be whiney, but that's really the only bad thing I can say -- this is the way OVAs should be, IMO.
Zeta Gundam was pretty much the best war story I've seen in Gundam. My roommate and I watched this over the course of about 2 months. We spent a lot of time trying to guess which character was going to get killed off when, or who would switch sides, and so forth. I think we spent more time cheering for the minor characters than we did for Camille, Char, or Amuro.
I'd have to say that Gundam has the better war stories, but I think the show gets too convoluted. I'm definitely not interested in trying to make sense of the various alternate universes. Macross is a lot easier to get into, and the music in the later series really adds to the enjoyment.