TV series.
First saw DYRL years ago, unsubbed (talking over 15 years now). I had heard of Macross, but never saw the original show, only watched a little bit of Robotech when I was a kid.
Again, I saw it unsubbed and in Japanese, so I had no idea of what was going on, but I thought it was GREAT. Just the whole epic "feel", the music and the GORGEOUS eye candy were enough to keep me interested. Plus I was about 15 at the time, so I loved the intense violence (especially the Zentraedi splatterfest during Miria's first attack).
But now, though, I watch a subtitled version online, and now I see that the story itself is really kind of rushed and there are a number of plot holes (some of which have already been mentioned, but my favorite is how Misa knows how to operate the computer system of a 10,000 year old civilization that she just discovered). But I still enjoy watching it, it certainly has a lot of great moments (the final attack is incredible, as is the Max/Miria dogfight), and visually it's still an absolute joy to watch. I still think it's the best looking "traditionally animated" (no CG) anime I've ever seen.
Now I'm watching the original series, and while the animation looks very dated, I'm amazed at how much thought really went into the story and the characters. I just finished episode 20, and I love how the show is hitting a lot of different storylines at the same time, in an intelligent way. The way Hikaru and Minmei are drifting apart, with Minmei off making movies and being a big star and Hikaru dealing with the fact that Kakizaki and Focker are dead. The way that UN Spacy is so cruel to the Macross and its people, using it as a sacrificial lamb and political tool rather than let the civilians off, and the way that they told everyone else on earth that the inhabitants of South Ataria Island are dead. The way Captain Global has to give a press conference with a heavy heart, telling everyone that they are being forced by the UN to leave the earth within 24 hours.
Sure, there are a few things that are a little cheesy(the ability of the city to recover from almost any attack, without any limit on resources or whatnot, for instance) but it really is on the whole smartly written and nuanced. As a character drama, a love story, a war story, it really is hitting on all cylinders. Awesome, awesome show.
DYRL looks great, and I still enjoy it a LOT, but the storyline is so much juicier (and the supporting characters are much better defined- Kakizaki had, what, two lines in the movie before he died?) in the TV series that I have to give it the nod.