Well, from what I've read the most common problem with the Shimano hubs is cable tension. As the indexing happens at the shifter, if and when the cable stretches or otherwise goes out of adjustment you wind up with missed or partial shifts and after a while a dead hub if not addressed. And that's with the 8 speed. I could only imagine the problem would be worse or more common with the 11. The Di2 places a motor at the hub in place of the spring loaded cassette joint so indexing happens at the hub. Rohloff hubs index at the hubs and have 2 cables to pull the cassette joint in either direction, so cable tension and adjustment doesn't effect the indexing. That's probably a factor in why they last so long for so many people that have them.
So far shifts with the Di2 are accurate all of the time. Shifting is lightning quick, and I only have to hesitate on the pedals for a fraction of a second between gears. Di2 is also the only option for a hub gear if you want to run integrated road shifters. I've been riding this set up for a month and so far it's pretty great.
This is my first experience with internal gear hubs, so I can't tell you how much better this is than a cable system. So take my answer with that in mind.