There are just a few points in which they differ from each other:

1. The Inner Monologues:
What the movie didn't include are the inner monologues of Gook and Taejoo, which I really loved in the series. But what surprised me was, that even tho they left them out everything still works perfectly fine, just because of the amazing acting. You'll notice that even without words you can just read everything from their faces and that's honestly so impressive.

2. The Music:
The movie gives of a different vibe mostly due to the different soundtrack.
In my opinion it was a bit more intense and emphasized the emotions of the characters better in some scenes.
What made me a bit sad was, that the part of the soundtrack which I personally love the most wasn't present in the movie as much as it was in the series (I'm talking about 'Light' by KEUM JO). In the series it was playing at the end of every episode and I loved it so frickin much!!

3. The Transitions/Cuts:
The transitions were different cuz (obviously) they can't just mash everything together and call it a movie.
Some scenes where cut short while some were a little longer than in the series. And it honestly didn't bother me at all!
I think everyone can see how much thought they've put into how to assemble every cut/transition.
Everything just works together very well

I myself watched the movie after the series but I guess the order doesn't really matter! Both versions have their charm and are definitely worth watching!