Yea, I considered getting the 2X III TC for my 70-200 IS II, but having used the Sigma 120-400 a while back, I am SO very sorry I sold it....and for dirt cheap too(like $650..
)..
That lens was simply wonderful to use and produced some really quite amazing IQ..actually, I would go so far to say that other than my 70-200 IS II, it was my second favorite lens..even though it was a beast to carry around.
Having now gone full frame, and knowing that the two have nearly identical performance(AFAIK, and in many different ways; IQ/OS/AF speed/etc/etc), I would definitely go with the 150-500...
if using a 1.3 or APS-C crop, the 120-400 is more than enough reach for me...and the little bit of weight makes a huge difference, to me.
I dont think you could go wrong with either...imho, and YMMV!
Good luck!