Amazon had to deal with customer acquisition and customer retention, while Groupon has the added challenges of merchant retention and margins being squeezed by competitors in a sector with relatively low barriers to entry. To me, it's a steeper uphill climb for Groupon.
The way that Groupon has defined the sector actually does present fairly high barriers to entry in that you need a dedicated sales force to 1) discover potential merchants and 2) arrange a deal that will work for the Groupon purchaser and the merchant. If someone redefines the sector by successfully removing the need for that sales force while maintaining the satisfaction of merchants and consumers, they will crush Groupon.
BTW, I think that's exactly what Groupon's competitors will do and are doing. Heck, all they have to do is steal Groupon's previous merchants now that the trail has been blazed.