I think it mainly comes down to cost vs. performance (optical and AF). At the bottom end is the Opteka/Bower/etc. 650mm manual lens that comes with a 2x TC; it's a fully manual fixed f/8 (1300mm f/16 with the 2x) and costs $250. The Tamron is arguably the most cost effective way to get to 600mm with decent IQ, although the lens isn't at its best at the long end wide open. The Sigma 150-600S appears to deliver much better IQ, but it's creeping up in size/weight. Pending some actual reviews, the 400/4 DO II is looking like an excellent option, with the 1.4xIII you have 560mm f/5.6 and the IQ should be excellent based on the MTF charts (but reviews will show things like bokeh, etc.). The DO is also significantly more expensive.

The 300/2.8L IS II with the 2xIII also delivers an excellent 600mm f/5.6 in a comparatively small/light package...but also a costly one. That's the way I'll likely go, but mainly because I already have a 600/4 so the 400/4 DO II is less interesting than having the option of f/2.8 for indoor sports along with a 'small and light' (compared to the 600/4) 600mm lens.

The other option that I'd be considering is the 100-400 II + 1.4xIII. You lose 2/3 of a stop compared to the Sigma 150-600, but the MTF is pretty impressive for the combo. It's a lot smaller and lighter than the Sigma option, for me a truly portable lens (like the 100-400) would tip the decision if the IQ was not too different.