I use a separator. Shell-to-shell has led to too many broken yolks in my experience.
I do agree with the advise to use a separate container for the current egg white - if a smidgen of yolk DOES wind up in that container, you haven’t ruined the whole bowlful of whites.
Separator annoyance though: none of them are really shaped right to rest over a container. One had a slit on the edge so it could hang over a cup - but fit none of my cups. Like this:
O|====
Another one has a slightly rubberized handle, and a bit of a lip on the “bowl” portion, but it’s not enough of a lip to be stable and it’s too easy to knock over - like this:
=O====
The damn thing needs to have a 3ish inch extension on BOTH SIDES of the egg-holding portion, like this:
That’s the starting point from where you must travel to get to the yolkless (or yolk-only) egg.
On a different subject, I kinda want to separate a couple of eggs this way, then cook the whites in one pan, and the yolks in another pan, and plate them together.
I used to do the pass it back and forth between the half-shells until I saw Meryl Streep in The Hours. She just used her hands and I thought, well, that makes more sense.