Apps don't support multiple tabs.
I'm rarely looking at 1 restaurant at a time, I'm trying to compare 5, or 6 or 10.
The Yelp app has no means of doing that.
Also, I can't easily select some text in the app, like the name of a dish I'm not familiar with, and quickly trigger a web search in another tab to do some quick side reading.
I have the Yelp app installed, but 9 times out of 10 the browser is how I prefer to use search for restaurants.
Because of Yelp's frustrating site restrictions, I find myself often using Google instead, even though I prefer Yelp!!!!!!
How ridiculous is that!!
Browsers also seem to have better low bandwidth performance than most apps. Probably because doing constrained network communications is hard and only browsers have the billions of reps needed to practice getting it right. With most apps I find that network handling in poor network situations (like is all too common when traveling and looking for a restaurant) is inferior to most browsers.
So yeah, Yelp would definitely win me over if they kept their site browser and low-bandwidth friendly.