Powder is better for the machine (less build up of sludge) and more effective at cleaning and killing germs (bio powder contains bleach, liquid cannot contain bleach for one reason or another).
On the continent there often isn't a difference between bio and no-bio (almost everything is biological), however, there doesn't seem to be a bigger problem with eczema. My dh has got eczema, in the UK we used non-bio, now we use bio and it doesn't seem to make a difference. However, I only use one scoop of powder and then add one scoop of Oxy Vanish plus I always use the long program (so lots of rinsing involved).