The attacks on the Minecraft and EVE servers were DDOS attacks. Nothing sophisticated, and the easy way to avoid them is to just get more servers, which really isn't a good solution for smaller developers.
EDIT: I suspect the only reason they didn't succeed getting to Blizzard is because WoW was down for Tuesday maintenance.
I suspect the reason is simply because they don't have the resources. EVE maxes out at about 35-40k simultaneous connections, WoW is probably closer to 400-500k per region.
They targeted the EVE login server however, and I doubt that is designed for 35-40k simultaneous connections, as to acomplish those conditions, all users on the server would need to log in at the same time. The same is probabaly true for WoW.
The login server for WoW easily and routinely handles an incredible number of simultaneous connections as huge percentages of the player base attempt to log in at the same time, particularly after a large patch. There used to be incredible issues with the login server, but these days Blizzard is an extremely tightly run ship. They know where their money comes from, and what it takes to protect the cash flow.
EDIT: I suspect the only reason they didn't succeed getting to Blizzard is because WoW was down for Tuesday maintenance.