Even though they operated at a loss while taking investment, they weren't using the investment to pay out older investors. They had a solid plan for generating profit, which Groupon doesn't seem to have.
Supposedly, they've been having a good deal of trouble getting repeat customers, they need to find new shopkeepers each round to make up for the last time. Hence why people are calling it a Ponzi scheme.
How does capturing more merchants drive their costs down, when they have to pay significantly more for each one?
Amazon had the answer of vertically integrating as much of the supply, warehousing, and shipment to drive costs down. Groupon doesn't have any way of driving costs down. That's the problem in my mind.
Scale is THE moat in this arena.
"Yet they haven't shown any way that scaling will reduce costs much."
This is simply Parkinson's Second Law: expenditures rise to match income. Hence the IPO. They need as much cash now as possible in order to scale as fast as possible to build that moat as big as possible to fend off the barbarians.
As the cost of getting more quality customers goes up you'd expect their costs in that area to proportionally decrease. And at that point, if they've defended their dominance in the deal-of-the-day market then they'll become massively profitable else if they're in a decent 2nd place then maybe Microsoft will buy them out for $5 bln more then they're worth, else they'll end up going the circuit city route.
If customers who arrive at a store through Google Offers are more likely to return to the store in the future without a coupon than customers who arrive at a store through Groupon, then stores will prefer Google Offers as a way to obtain loyal customers. And if stores prefer Google Offers to Groupon, then Groupon collapses. From the point of view of the merchants, this is all about getting repeat customers who will make up for the loss that they are taking on the coupons (or, in some cases, betting on customers spending enough in addition to the coupon to make a profit on the one sale).
The moat that Groupon needs isn't scale, it's loyal merchants who will offer coupons on Groupon repeatedly - which will get users to use it. If it can't get that, then it will burn out once it runs out of new merchants.
Who does the client go with? Much like with any other advertising the one that delivers the best value. Value here is defined as # of new customers divided by the lost revenue. This will ultimately be driven by scale -- if Groupon can sell more tickets they can offer a proportionally lower margin and will be more attractive then competing services.
However, you're completely right that clients would go with whichever service offers the best value and best range of coupons, and that scale offers an advantage there. I would add that it is highly unlikely that subscribers would only subscribe to a single service. With the marginal cost of subscribing being so low (just signing up with an email and then looking at the deals when they show up, as I understand it), the increased variety of coupons would almost certainly sway the majority of subscribers. At that point, it would become a fight over which service can find businesses offering the cheapest or most desirable deal, in which scale gives the advantage.