I'm for the one string at a time method myself, if you're taking all the strings off the guitar you will release a lot of tension that is on the neck, normally when you have your guitar set up or serviced by a guitar tech they will remove all the strings to file and dress the frets and also clean the neck but when they re-string the guitar they will do bridge and truss rod adjustments to make sure everything plays nice with the neck under tension. But even after these adjustments it can take a few days to settle in properly and further tweaks may be needed, remember the guitar is mainly wood and has a certain amount of movement to it.
It's only my opinion but I would personally minimise the amount of times you take all the strings off your guitar unless you are planning to make truss rod and bridge adjustments too