Okay first, neither eBay or google are a monopoly in the technical sense.
But in principle, eBay can defend its market dominance more than google.
Say there is eBay, and eBayCompetitor. eBay starts off with all the customers. As a single seller or buyer, I can chose to move to eBayCompetitor but it does me no good - if there are no sellers or buyers at eBayCompetitor except me, the site is useless.
On the other hand, if everybody is at Google and someone starts GoogleCompetitor, I can leave Google and GoogleCompetitor would work just fine for me, because it doesn't matter whether anybody else uses GoogleCompetitor. You could end up with some kinds of semi-steady state like in the browser wars.
The problem in practice with search engines is that I am starting to get the idea that the "market" likes having a single search engine to worry about/buy ads to/manipulate ranks for. So it is possible than in reality there is some pressure against GoogleCompetitor gaining traction.