to the OP
boot flex is as much a personal thing as is ski selection - and the 2 have an effect on each other.
if you have a fairly stiff ski (for your weight) and combine that with a fairly stiff boot, you'll likely find that absorption of dramatic terrain, like moguls, will get more difficult as you put in more speed. If both are very soft, then you may find yourself 'behind' on your intended line. There's a happy medium/combo for both. Extremes can provide extreme experiences.
SInce I generally don;t go hunting for mogul sections, unless it's a steeper section and in good snow, I generally like a little longer, stiffer ski. The longer, stiffer ski tracks easier thru rough snow. To offset some possible harshness and hyperactivity, I've skied with a slightly softer boot paired to stiffer skis. The softer boot flex allows absorption to be more even through my posture. If I was in a significantly stiffer boot and skied at my normal speed; with the ankle area giving less range, I would have to, dramatically, use more knee, hip and torso absorption for the same terrain.
Again, for me it's a matter of 'balance', at 167 lbs, I get bounced a lot more by a quasi-race boot. AS much as I now luv my Doberman 130 EDTs, I did take steps to tone them down a bit on stiffness, and like them much better now. If I was 200 lbs, I'd might be fine with them at the stock flex...
Not all flexes are created equal - My Fischers (heatfire-XL), listed as 105, are close to 120 (on my scale), I had a pair of Fischer RC4 RACE which were listed as 120, and felt the same as the 105s. I had already done a bunch of mods on the 105s, so I re-sold the 120 RACE, since they were skiing mostly identical...
POW - like ice, is best served with a delicate touch. On ice, a delicate feel for the edges works best for me. In POW, it's not edges, it's the planar surface, which can be harder to control well, especially in grabby, wetter snow, like our Sierra POW. The deeper you're down (deeper snow or narrower ski width) the less room for balance issues. I like that feeling of depth. So again, boot flex makes a difference for me in just about any snow condition.
At only 20-24 days a year, I sometimes feel 'imprecise' in my movement and balance, the little extra flex in the boot allows me that without causing major issues at the ski/snow level. I know what I need to be doin, but sometimes it doesn't happen.
If I find myself in a tough spot, the boots are solid enough for me to power through; but I like not having to constantly worry what the ski might do.
If you've had the boots for a while, a packed liner will allow more flex. A new liner, like an Intuition, will make a boot stiffer.
If you're moving inside a boot, that's a different issue.
Demo-ing boots offers a chance to feel your options, always a good thing