I have both and primarily used the 1.4 x TCII on my 70-200 VRII because my 2XTCIII made my D200 AF hunting too easily. I now have a D800 and use both as well.
N.B. I bought these TCs primarily for use on my 500 VRII where they perform excellently ( 1.4TC) and very very well (2TC). I have the TC2 III wich is known to be much better than version II.
Quality-wise, there is a visible difference between the two, but it isn't that big and practically disappears at f/8 or when downsizing from 36mp or do some sharpening.
Another point, as you know very well, the 1stop difference means slower shutter speed or increased ISO meaning potentially more blurred image or noiser image. This may be important for some older sensors (like my D200) or when handholding.
I have both and will keep both (useful for both 500 and 70-200). I would personnally say that the quantity of light available in your planned shooting environment and the required max reach are a more important selection criteria than final IQ.