Edit: Less than 12 hours, so not bad there. The item was 3000 JPY and they charged 500 JPY shipping (~$6), but the shipping from Amazon was not included, so I have no idea how they make any money on this. Another modest limitation of Buyee compared to Tenso is that you are limited to their list of stores. It is a pretty good list, but is missing some stores I find obscure things at.
It's really the same company - Buyee is just an additional service over Tenso. With Tenso alone, you do the shopping yourself - Tenso just gives you a mail forwarding address. I started using Buyee mainly for Yahoo Auctions; for Amazon I think their main advantage would be in case there's any interaction with the seller, they will handle it for you. A lot of Japanese sellers will *only* deal with Japanese buyers, and Buyee is a Japanese buyer. With Tenso, you're on your own as if you were shopping on the US site... all Tenso's doing is giving you an address. So some sellers might still not deal with you.
As for how they make money, first, they're going to add the shipping fee from Amazon on to your total shipping fee later, so don't be surprised when you see it. Then they just have a lot of little fees on top of that, some of which you might not notice. I just bought a CD from Yahoo Auctions that was 2500 yen, or about $23.56 at current exchange rates... I selected no additional service and still I ended up paying something like $27 and I don't even remember why. I'll also be paying a 1500 yen "consolidation" fee later, but hopefully I'll save on shipping overall by doing that (that's the point of doing it). But yeah, their prices are pretty reasonable I think. You don't end up paying all that much more than if you just bought something directly and shipped it here.