Not really relative but, kinda funny this was brought up. My cousin (bass player) asked me how I changed strings? I said: what do you mean, how? He said he cuts his all at once, OK. I told him mine are done one at a time starting with the "B" string. Tuned and then going to the "E" and so forth.
He asked why I don't just cut them all down at once? I told him it's just my way of doing it. I didn't like all the tension off the neck at one time. This way the neck should stay pretty much where I had put it to begin with, weather it matters or not how it's done? To each their own. All I got from him was a hmmm.
I used to do that, but I've done a lot of work on basses - mine and a bunch of other folks', including loads of setups and neck heat treatments for the extreme cases, and I've realized that necks are tougher than we give them credit for. I had strings completely off of one of my basses for a week and a half, and just restrung it with the same strings. It went back to precisely the same place (well within .001" in relief) - checked with a feeler gauge and a straight edge.
There may be some necks that are in the edge - if you have a thin neck, use heavy strings, and you have a LOT of tension on the truss rod, I can see being more careful, but with a good neck, they are much more forgiving than most folks think they are.
If the neck moves when you change strings, it's much more likely going to be because the new strings are different tension wise, not because you changed them all at once.

