Parallax adjust on a 6X is a marginal advantage unless used for bench rest shooting or something like that. These parallax adjust scopes commonly have very fine reticles that are not the best for hunting but great for placing shots one on top of another in bench rest comp.
Considerations are the field of view at a fixed range, say 100 yds. Some general values, give or take 2 feet or so, are: 4X - 30ft, 6X - 20ft, 8X - 15ft, 10X - 8ft, 12X - 6ft and so on. I don't know exactly but the stats are available before buying.
A 12X fixed power scope would be a liability on a white tail hunt in brush. But would be great for shots at long range, greater than 300 yds. Short range use with the 12X would require refocusing.
I do almost all of my deer hunting in open country either with an old 6X Burris Signature 6X40 or 12X Leupold 12X40 FXIII. If I had a relatively small compact 8X or 10X with parallax adjust and target adjustments I would use that. I like the extra magnification for use on the range, spotting bullet holes, and the occasional small target at extended ranges and would not feel at a real disadvantage should I have an opportunity to take a shot at a standing or slowly moving deer at 30 yds or so. That's the only kind I shoot at.