It depends if the brand you change to uses a different grade of steel to make up the string. Especially the central core.
Steel can be made with different proportions of iron and carbon. The more carbon in the mix, the harder the steel. That's a reason why stainless steel strings are tighter and also wear your frets out faster.
Anyway, you're not changing to stainless are you?
Even so, the difference between two brands of nickel plated steel strings of the same gauge won't be much if anything at all, even if the steel they are made from differs.
If your neck relief does change that slight bit and you want it to be *exactly* the same as it was before you changed, it'll only take a really small turn of the truss rod. I'm talking about like one eighth of a turn.
