Does it affect the kind of artifacts you get if you collect artifacts one by one or all in one go?

Also, which method do you use for collecting artifacts?

It makes zero difference. The "Collect All" is essentially a loop that collects them 1 by 1 and then feeds back the result.

As far as I know it doesn't make a difference. I collect all in one go to save myself from clicking.

It's just that I hardly get MSPs when I collect all in one go and ever since I did it individually a few days, I've gotten 3 in 2 days.

Coincidence?

Yah that's just coincidence, and yes it makes a small difference.
Pulling individually will give more prisoners, and less small things like cloning pods.

What KJ said about the difference is only correct if you manage the AP correctly. Otherwise, it's the same as far as I know.

the only difference it can make is if you stop collecting after you drop bellow the threshold for another arti let it fill up again and repeat. Eg you collect till you go bellow 4k and then wait collect again. increases chance of prisoners