Interesting. They're both really in the same category for me.
I knew a ton of each as a kid, but they're less common on babies today.
Honestly, I think I like them both equally.
Do you prefer Josh over Matt or vice versa?
I think both names would fit nicely in with your family.
The only real difference is that Joshua is an old testament name like the others you've listed while Matthew is not.
But Joshua would repeat a letter which I know some people don't like.
I can't really give you any reasons to go either way.
Personally I would probably pick Joshua, but that's because my BIL is named Matt so that would be sorta weird, lol. Not helpful to you though :)
I would go with Joshua.
Matthew gets my vote. Good luck!