>>18 The show is a collection of a few 6 minute OVA's, and it's really just the first part of the movie (up until just before the gov't finds out about Patema). They re-vamped the art when they went to do the movie but kept the same scenes, which is why the beginning of the movie seems very detail heavy on the art.
I think it's good to watch both since the anime won't take much of your time and can show the interesting details between adaptions.
The anime also shows things in a different order than the movie with slightly different words. Quick spoilers for the movie below.
For example, in the anime, Lagos is shown early on telling Patema that he was going to be gone for longer than usual and gave her the picture. She was also a child all the way through the flashback. In the movie, they didn't show that scene until later on, and he instead said that he would *never* be coming back because his dream couldn't be fulfilled. Patema also got older halfway through the flashback. That makes it seem like it's an illusion or dream (and would explain the plot hole), but the lack of the original flashback prior makes it seem canon.
This caused a few plot holes. Lagos saying that he couldn't fulfill his dreams means that he came back after Age's father died, but they show in the final version of that scene that the enforcer characters saw Lagos when they killed Age's father, which implies he was caught then and couldn't have gone back. Because of that flashback, we have to assume that he actually *wasn't* caught and went back to see the underworld one last time, but that doesn't make any sense either because the scene still showed he left with the tubes used to float Age's father's device in that flashback (which were also seen by his corpse) and means that that visit must have been before his death.
I originally thought he came back and left to get revenge, which was how he got captured, until I noticed those details.
I wish they just kept the flashback as it was in the anime or made it more obvious that it was Patema's dream. It created such an awkward plot hole imo.