I have downloaded from both Steam and the Blizzard Store.

Steam
I personally hate the Steam interface. The program takes a long time to load up and connect. However, once its up and running the system works pretty smoothly. There are a very large number of games for sale through Steam, and the prices are acceptable. The biggest positive for Steam IMO is the download speed. I'm not entirely sure what kind of a download system it uses, but it goes at absolutely blazing speeds and it doesn't seem to hog many resources. Installing games via Steam is actually far easier than doing it with the physical discs. In addition, Steam remembers what you have bought and allows you to install it on multiple computers as long as you've got the same account. This is very useful and convenient.

Blizzard
I have only downloaded Diablo II and the expansion pack from them. The interface is very fast, since it's all done via a web browser. You buy your game, they send you your CD keys, and then you are provided with a link to the downloader utility. Each game has its own downloader utility. You run that thing, and then it starts to download the programs for you. The speed is decent, though not as fast as Steam. All around, an acceptable service, though the selection is limited to Blizzard software AFAIK.