As someone who has composed before, I tend to take a chord progression and then fit a melody over it. It's a lot easier than just doing it all from scratch.

As a musician, I can safely say it's much harder to find melody to match lyrics, because you've usually written one or the other first, but it's at least easier to match lyrics to melody than melody to lyrics.

but i see the struggles of the other option too

I'm not trying to diminish Bruns' fantastic work in Sleeping Beauty, though. He turned the score of a comedic scene involving cats into "Maleficent's Evil Spell", after all (yes, I'm aware that the question refers specifically to the relation between melody and lyrics, but I thought it was worth mentioning).

As the most musically inept person on the planet, I don't feel qualified to answer this. My guess would be that creating original music is harder though.