Hitomi wanted to just disappear from her life. The track club -- her best friend -- her parents -- she wanted it all to just...go away. While contemplating suicide, her wish is fulfilled by an unlikely savior: a man named Folken who brings her to his world, Gaea, to unlock the powers of the legendary Dragon, Escaflowne. But there are those who would stop at nothing to foil his plans, and chief among them is Van, the last warrior of a noble clan. Caught up in this epic struggle, Hitomi must find herself before she can find a way home.
It is not just that these are movie retelling of respective series, but both are changed quite drastically.
I would say, that if you had not seen the series that connected the movie, you would not need to.
Both stories have a girl who is the major key to the story. There is a romantic notion in both, and the animation in both are of high movie caliber.
If you liked one, you would most likely enjoy the other.