My laymans understanding:
Standing whilst climbing [produces] more energy, but also wastes more energy, due to breaking traction ... which is reduced (not eliminated) by shifting your body back and forth, which, wastes more energy, and upsets the rhythm of your cadence, which further wastes energy.
The benefit of Clipless is that you can stay seated and generate the same (or consistent) cadence, with reduced body shifting.
Staying seated whilst climbing has been found to be the most economical method for dual suspension rigs.
My Personal Experience:
I tend to push my pedals forward (starting prior to the crank arm coming vertical) and down ... and rarely pull up (unless I'm tired).
In technical terrain, especially technical climbs ... being clipped in allows you to bounce or lift the rear, allows you to half pedal at more varied angles, and forces you to try harder so as to avoid having to unclip (you all know what that means ... oh oh, can't get shoe out ... tiimmmberrrrrr)
When I'm tired, I actually pull up more to assist (I know its counter intuitive, but thats what I do for some reason).
With flats, I can follow this same stroke when I'm fresh (and with 5.10s) but not when I'm fatigued, which doesn't take long. (5.10s are heavier then clipless shoes in the majority of occasions, and its rotating weight, which is bad)
In flats, when I'm fatigued, I smash more, and my feet slip off more often, which means Mince Meat Shins. (leg armour is hot, which is bad and smelly).
Similarly when fatigued, I tend to bounce more, due to poor line choice and or poor pedal pressure ... more mince or worse, smashing the knee onto the stem ... ouch.
Sooo, personally being clipped has more pluses IMO.
Re: Knee Pain ...
Have you got your seat up as high and as comfortable as it can go ?? More seat height reduces the amount your knee has to bend ... whilst also helping with the pedal stroke.
With my pedal stroke and being clipped in, my weight is transferring to my other leg (power), as my leg (returning) is shifting towards the vertical or bottom of the stroke, which means I'm not putting pressure on the joint.
I'm not sure if I'm unique with this stroke, but from my understanding this is the theory behind elliptical chain rings, which apparently the majority of people, including professionals can benefit from (a whole different thread I know).
Lastly, what pedal system were you using when suffering your knee pain ?? I presume it wasn't Time or Crank Brothers ?? If I'm right ... maybe worth trying the Time Atacs ... you can get the Aliums for dirt cheap on ebay.
Anyway ... good luck, maybe somethings in there re, technique and or equipment choice to consider, whilst your on Christmas holidays