The type of ammunition & magazine used for a given weapon affects four things:
- damage (not usually any change)
- loaded ammo count
- total ammo count
Weapon type also has an impact on these, as do other attachments, and as far as I know, ammo doesn't affect accuracy.
It comes down to common sense - what ammo will give you the best damage & penetration for a given weapon while enabling you to carry enough of it to actually use it?
Sniper rifle ammo (like .308 for instance) in an assault rifle, while giving you great penetration, will quickly be spent when you can only carry 25 rounds of it.
Contrast that with using 7.62mm assault rifle ammunition instead of .308 in a sniper rifle - the penetration more than halves but the damage stays the same, and you can carry hundreds of rounds instead of 25, with bigger magazines. Might be a good choice when going on a long op where you wont be shooting people through cover, or they are unlikely to be armored, or like me you just like the sound of sniper rifles and want to make more noise.
The weapon customisation in MGS5 allows you to do almost anything, but that's not to say that anything it lets you do is a good idea.
In short, using sniper ammo in the G44 will do three things - it will raise penetration, lower your ammo count, and allow you to spray every bullet on full auto. But only once.