From a user's perspective, after describing your company as the "Airbnb of pet sitting" you may have to follow that up by describing what Airbnb is. My parents (the benchmark by which I judge all potential customers) would have know idea what Airbnb is...but they do know that their golden retriever needs a cheap place to stay while they go on a cruise next month. So the best way to describe it to them is:
Stayhound - we use social connections to help pet owners find pet sitters for less than kennels charge
I can't speak from experience with investors, but to me describing your business as the "X of Y" makes it sound derivative, like the old style of movie pitches (e.g. "it's When Harry Met Sally meets Beetlejuice...on the Titanic!"). I think it's better to succinctly describe your product or service, while avoiding marketingspeak or names of other companies. Of course, investors may think otherwise.