A few months ago I had to make the same choice and I picked the 200-400/1.4x. I do not regret this choice.
Ultimately it really boils down to what you like to photograph. I use this lens for a wide variety or purposes - wildlife, sports, and landscapes. For these purposes there is no contest - the 200-400 is the best lens that can achieve all three.
If I were only photographing wildlife, or more specifically birds, then the 600/II would be the better choice. You simply need as much length as possible. If an 800/4 existed that was actually portable, I would recommend that. That being said, you can certainly accomplish a lot with 560mm.
For a real world example see this set http://www.flickr.com/photos/calevphoto/sets/72157641149672084/
Three of these images were taken at 560mm, but three were not. The versatility of the 200-400 certainly wins out here.
For sports I almost never use the extender. I also find myself switching a lot between 200mm and 400mm. It is one case where a zoom is invaluable.
Finally for landscapes I am all over the place. That was really the deciding factor for me. I wanted a lens I can use for landscapes to catch the shots many landscape photographers miss. For these I rarely shoot at 560mm.
This set illustrates the flexibility - http://www.flickr.com/photos/calevphoto/sets/72157640572094314/
Most of the landscape shots were not taken at 560mm, while most of the close up bird shots were. A 600/4 would have probably done an even better job, but the 200-400 certainly did a very good job.
Someday I may pick up a 600/II if I have a sudden influx of cash, but it is not a huge priority given the excellent performance of the 200-400 at 560mm already.
BTW, the Tamron is a very nice lens, but the 600/II and 200-400 are in a completely different class. There are vast differences in AF speed, image quality, and the extras that go into a top end lens.