I don't think it could be Tears to Tiara as that show is fairly recent.
I really don't think that it is Jyu-Oh-Sei: Planet of the Beast King either. I sincerely hope not, as that show was horrid. It was also dubbed by Funimation, which should rule it out, but if not, I don't remember any giant-sword battle scenes like the OP described. I remember a ridiculous time skip, the main char Thor being a wunderkind, a lot of bromance, and a final battle against
Warning: Spoiler!giant genetically engineered plants
. I remember that there was some minor love triangle thing going on, but the main character saw one chick in a sisterly way (and was uninterested, it's not Oreimo) and the other one didn't seem to get into a scenario like the one described by the OP. Most of the show took place in an undercivilized world, in clay buildings in a jungle.
But since you mentioned a show that was even worse than I was thinking of, I have a slight thought that it could be Lost Universe. It has older art that is semi-realistic. It was dubbed by ADV/Sentai, and it kinda had swords while still being scifi. I don't think that it is what the OP seeks though as I don't remember that exact scene, but I also don't remember if I saw the whole series.
I mean, it
has to be an ADV show, right? How can this be so hard?