The more I think about it, the more I think it's related to the network code. Heroes of the Storm is fucking terrible at the moment, and any form of network spike causes in game frame loss, as in, the game slows down to "keep up" with the network traffic. This causes frequent pausing and stuttering. I'm willing to bet both games run the same network layer or something.
D3 was shitastic at launch, and with the launch of RoS (and aussie servers) I had very little stutter. It's still there though in bigger fights, and more players.
The worst I ever had it was on the Bridge of Korsik, crossing that was a fucking slideshow, while a friend of mine never had any problems at all. Seems much better these days, but I still actively avoid that area.