I am hardly an expert, but I've had (and serviced) both a 1 pump GE model (cirica 1993) and a much newer Frigidaire (aka Electrolux -- European company) with 2 pumps. The newer model was not 'top of the line' -- I think cost was like $350 to $400. The design is quite simple with 2 pumps, and avoids solenoids and flaps that the GE model had. I had to replace the expensive pump/motor assembly on the GE (about $120 as I recall) due to a motor failure. I did have to unstick an impeller on the Frigidaire (the drain pump, not the wash pump) as a piece of glass was caught in the impeller -- but didn't break the pump (cheap fix -- just my labor -- and I'm cheap).
I don't know share of market for the 2 designs, but looking at the parts, I don't think the 2 pump is more expensive than the 1 pump. The cost of a small pump motor isn't a lot, and simplifies the mechanicals a lot.
I don't know who else uses the different design approaches -- if you knew this, you could probably infer market share as most of the models share most of the basic wash components among the product family.