If everything is identical, pics, copy, price, keywords and so on ..... then I would suggest it would come down to two things. One being the different level of competition you are facing between sites. Number two, and what I suspect would be the main cause, traffic. Yes, Priceminster may well have a lot of traffic, as you say, but they don't match eBay's flow.
More traffic at the very basic level, translates in increasing your chances of being seen and making sales. If you throw a stone at a grouping of 100 wooden ducks from 20 feet away, your chances are hitting at least one are increased over hitting one from a grouping of just 5. Of course it takes a lot more than traffic on it's own to create sale, but if you are throwing where the ducks are thickest, then you're increasing your chances straight off the bat.