How closely does the World Trigger anime follow the manga? I have recently started watching the World Trigger anime and I have liked it so far. I read that the manga was way better so I'm thinking to switching to that.

However, I've been wondering: are there any big differences between the anime and manga?

For what it's worth, with the anime, I have just finished the second large scale invasion part.
It appears that there is little to no major plot differences, with 1 of the 7 story arcs being anime exclusive. However, there are 15 characters exclusive to the anime and 1 area that is exclusive to the anime. Considering that you claim to be at the 2nd Large Scale Invasion part (lasts episodes 22-38 and chapters 44-85), assuming that the second part is halfway through the large scale invasion arc, then you would be around episode 30, doing a simple ratio calculation:

(16 / 2) + 22 episodes = (42 / 2) + 44 chapters;


And you would probably be around Chapter 65 in the manga.

Further Reading:
Here's an article on the Story Arcs
Here's a general article about World Trigger on Wikipedia