I'm surprised that there isn't much competition. I was traveling recently, and found Zomato's app to be much superior.
Two rather signifiant UX issues on my end are:
1. bad image resolution (do they resize pictures to be smaller?); this is also worse from yelp.com
2. Why is the regular swipe from edge of screen to go to the previous screen overridden to move from review to review? (same issue with GMail app though too)
I completely share your frustration here. I actually met a Yelp iOS engineer once and asked them about this. They said the idea is that it's supposed to feel like the way you navigate photos in albums on iOS; their expectation (whoever designs Yelp's iOS UX) is that users want to read many reviews and don't skim the review previews first to find the ones they like.
I showed them how I prefer to browse reviews: skim the previews, find a promising looking one [Yelp review signal/noise is terrible], "drill into" it, back out, continue until I've read enough reviews to make a judgment. They said they understood my POV, but stood by the assertion that most users don't use the app this way. Maybe they have metrics to justify that.
I can understand why they'd see it that way. But my preferred UX is exactly what you described. I want to find a review that looks like it may hit on what I want to read about specifically, and then exit out as needed.
Twizoo is also a new competitor that takes a completely different approach by getting reviews from Twitter. It also uses a data visualization over lists which is interesting. However, I think it's only live in a handful of US cities.
In Europe, TripAdvisor is probably the #1 most used app in this market. Although I don't personally really like it either, not so much because of any technical problem, but because they've chosen to be extremely annoying about nagging you to create an account, which I don't have any desire to do.