Five Star Stories

Very similiar animation style. I only watched the raw version of Dragon's Heaven so it's hard to compare stories, but the mechanical design is so similiar and I feel if you like one, you should like the other. Hell, they are both only about an hour long so it's well worth the time to check them both out. 

Both titles have mechas, but the story focuses more on the romance. Somewhat similar art style 

These two films hold similarities in being the beginnings to extremely long and complex stories that span lightyears and hundreds of characters. While LoGH aims for the more realistic depiction of war, FFS has a more flamboyant style and story, but remains just as broad in scope and detail. Both films also are relatively contemporary to each other, also both are more or less an hour long. 

DYRL and FSS are similar in that they both sort of through you into the situation without a whole lot of backstory, it's probably assumed you should know what's going on already by having seen their previous adaptations. Both are mecha anime, although the focus isn't entirely on the robots but instead on the characters and their situations. Other than that, both feature great animation and coloring, and haven't aged that badly over time. In addition, both are considering space operas and both are the beginnings to their much longer respective stories.