Neppuu Kairiku Bushi Road

very similar plot. post apocalyptic world with monsters overpowered side/main character with monstrous capabilities 

They both have that adveture feel . They need to go to one place and do something and the anime and special are showing the same thing. A weird creature that isn't human helps human ( or way around). The both characters evelop feelings and without any kissing scenes (at least at the beginning) we can obviously understand that they aren't just simple friends or something. At least one or other began liking. The story and characters are really interesting and it doesn't make you bored other way around, it makes you keep your eyes focused on the screen until you finish it. Their both ending sucks and I will repeat myself " why can't both characters die , but only one?" . Yet it has the feels and cute moments and you won't regret time while watching it. read more 

Drastic event changes the world as we know it - in this case it's killer plants - and years later the story follows someone who's fate is to undo what evil has been done. Both have action packed moments, moments of touchy-feely love, and monsters (because who doesn't like those).