Escaflowne

Both are condensed and dark, twisted retellings of their cute, fun, and fantastical shoujo anime counterparts about schoolgirls being transported to another magical world that they have been chosen to save. Not to mention both are about magical girls and mechs that are actually living beings- In both cases, the mechs are actually dragons (or a bird and a lion, in the case of the 2 other mechs in Rayearth). The only notable difference is that where Escaflowne has a male and female hero, Rayearth has 3 heroines.  

Both have a female lead who at first seems like a regular high school girl but can actually see and travel to another world. Both have hidden powers, and both try to help the male lead. Both male leads need them to save their world. Both male leads hold power in their world. Both female leads get caught up in an epic battle. Both Movies have a series counterpart.  

Similar main characters, living in present day Japan, dissatisfied with their lives, are transferred to 'sword-and-sorcery' world. There they find that prophecy is awaiting them, according to which they should save this world. In "Capricorn" main character is male while in "Escaflowne" female. Both shows has dragons as one of the main aspects of the world. The main difference is that "Escaflowne" is much better one. In fact "Escaflowne" is, what "Capricorn" could be, if it was made properly. 

Just as the Adolescence of Utena, it removes unecessary and idiotic plotlines and capatilaizes on the originals strength. Also develop romantic relationships correctly. 

Teenage girls who lives unhappy in comtenporary Japan travel to another world because she's the chosen one, despite she doesn't want to, but while she travel that world and learn more about it, she start to get more self esteem 

Magic and mecha are the combo that brings these two together. Escaflowne portrays magic in a more traditional way with wizards, spells, dragons, etc., and Break Blade takes a more scientific approach. Both are enjoyable shows with a decent amount of action and just enough drama to sweeten the story. 

both are maybe the last of mostly animated feature films back in the after-millenium years that in my eye are damn good anime films before mostly digital and 3-d animation kicked in. 

Both of these have beautiful artwork and very pretty music. They also feature something of an unusual fantasy theme, something not quite as bubbly as your average shoujo. 

I think the main plot is very similar. And I also got the same feeling from the music, which sets a beautiful atmosphere in both movies. If you liked Escaflowne, you might well enjoy Nausicaa even better. I sure did! 

Both films are beautifully animated big budget adaptations of earlier classic mecha-series (both with Shoji Kawamori involved in a major way). With an emphasis placed upon darker and more realistic animation and tone alongside an intangible and alluring mysticism, each work strengthens their respective franchises.  

Two love stories involving alternative worlds and giant robots. I also found that both had very moving scores and similar pacing. Both are movies based off of anime. 

Similarity : + "parallel world" is exist + In the beginning story MC forced teleport to another parallel world and later treated as "savior who will bring victory" Different : + Dual Parallel have harem element & set in modern day + Escaflowne dont have harem element & set in ancient time