Probably an important difference would be that while Yelp users are almost by definition looking for new experiences, Groupon users are likely to be either people looking for cheap new experiences, or people looking for any cheap experiences. I mean, be honest, if price wasn't regularly a big deal to you, would you spend much time on Groupon, where the options are drastically more limited?
That is to say, the difference between running a promotional discount in a regular magazine, and running a promotional discount in a coupon magazine.
That is a very good point. In the one case (Yelp) they were advertising a good 'first visit' deal to folks who were already looking for their services. In the other case (Groupon) they were advertising to a group of people looking for cheap deals, not even people who were looking for their services. It is odd that the NYC business list (can't recall the name at the moment) is also a 'deals list' type of service and a similar discount to Groupon was offered but it had much better results. Checking them out myself at the time, the NYC business list seemed to be much more centered around getting a customer in once and keeping them as a customer and seemed to cater to a different demographic than Groupon.
I use Groupon for experience discovery. I could spend time combing Yelp for new restaurants (and sometimes I do), but it's nice to hear about a new one through Groupon.
Perhaps, but it also means that the pool of potential new experiences is being limited to businesses that just did a Groupon. I'm sure results vary widely, but in the aggregate that probably has implications for what can be expected of both the seeker and the provider of said new experience.
That is to say, the difference between running a promotional discount in a regular magazine, and running a promotional discount in a coupon magazine.