If I may, I'm not sure it is accurate to say that one or the other is more highly deoxidized. Though it is more often understood as S2 being more highly deoxidized due to the triple deox Ti, Zr, and Al, which, as far as I know more readily bond with O2 than the Si or Mn of the 6 (the same reason 321 SS fillers are seldom used-if even available-the same reason Al must be AC welded, and quickly after preping-and the same reason Zr and Ti alloys are so sensitive to purging).
But it depends. I think you would have to venture into thermochemical reaction studies to verify one way or the other. Not my bailiwick to be sure. 2 is often recommended for material with highly oxidized layers, such as rust. But the triple deox elements will build up in multipass applications causing visible non metallic deposits.
6 will generally demonstrate higher strength and lower ductility. But they are most often readily interchangeable. The most important issue being exactly what Marty posted. Make sure than within the context of your WPS that you are actually using an A-1 chemistry. Not that it risks the viability of your weld, but you will have violated your procedure.
Just one of those quirks caused by the fact that the Section IX guys aren't the same ones as the A5 guys.
And Walt and Marty are correct, there aint no A# with high Mn S6.