After watching the Macross Frontier series, I decided to also give the movies a try. There are two, The False Songstress and The Wings of Goodbye. They might as well have just gone ahead and called them part 1 and part 2, as they're really two parts of the same story. The movies are an alternate version of the Macross Frontier story-line, not a continuation.
The obvious difference with the movies is a significant reduction in time: 4 hours of movies vs 25 half-hour episodes in the series. That requires some changes in plot - more on that later - and also dropped lots of side stories. No Miss Macross competition, for instance, or trip to a Zentradi outpost planet. This eliminates a lot of the slow start that the series suffers from, but also means very few of the supporting characters have any depth. It also means that there are minor references which may not make sense to a non-series watcher - for instance, the byplay between Michael and Klan.
There are significant plot changes in the movies. I found it pretty difficult to follow the high-level story in The False Songstress, to be honest. On the personal level it made sense, but it was difficult to understand what the Macross Galaxy people were trying to accomplish, much less the alien Vajra. Having watched the series might have actually hurt me here, as it was easy to assume things about the characters' motivations from what I'd seen in the series. But I think the main culprit was that the writers were trying to keep from revealing too much about The Wings of Goodbye, because the story got a whole lot easier to follow in the second installment.
I won't go into spoiler-level details about the changes, but I will say that I thought the series did a better job with the big-picture plot. To some extent, this flows from the difference in length - it's a lot easier to convey a complex plot involving many different actors when you have more time. However, I think the movies did a much better job resolving the personal relationship between Alto-Ranka-Sheryl. The series ending felt unfinished (perhaps intentionally, to leave room for sequels), while the movie ending is much more concrete.
I have to mention two things added in the movies that stuck out, both from The Wings of Goodbye. First, there's a concert given by Ranka in a prison (weird, I know...it makes sense at the time) which has a ton of references to Fire Bomber and Macross 7. I may not have liked the series much, but that scene was pretty cool, from the "Lovely Bomber" stage heading to Klan wearing Mylene's on-stage getup. Second, the Macross Quarter manages to survive entry into a planet's atmosphere by landing on a big hunk of rock and using it like a surfboard, complete with Captain Wilder making surfing-related comments. Now, I'm an old-school Transformers fan, so I'm used to giant robotic shenanigans of all kinds, but that one was just so totally out of place that it floored me. I'm pretty sure the writers meant that to get a laugh and then just kinda fade into the chaos of battle, but I had a hard time getting back into the "gigantic climactic battle" feeling after seeing that.
On the whole, I think I prefer the Macross Frontier series, but it's close. The movies are well done, and it's worth watching them if you don't have time for the whole series, or if you're curious about the differences.