Depends on how much reach you need. The 2x on the 300 f/4 probably won't autofocus, not letting in enough light. The 1.4x is, I believe, a little sharper. I had one, actually, but I took it back. I was using it on the 70-200 f/4, and not getting much use at all out of it.
1.4 will turn your 300 into a 420. Then with the 1.6 crop factor, that's the equivalent of what, 650mm on a full frame sensor? The 300 will autofocus with the 1.4...
The 2.0x with the 70-200 will need to be stopped down 2 stops (f/11) to recover sharpness. It will be pretty soft wide open (f/5.6). The 300/4 with the 2.0x will not AF except with 1-series bodies (max aperture is smaller than f/5.6).
You're going to be more satisfied, IMO, with the 1.4x. You only lose a stop instead of 2 stops, and you lose less sharpness, plus your 300/4 will AF with your body.
I've been very happy with the 2x - I've had some pretty decent results with it on the 70-200 2.8L IS.
It seems to retain it's sharpness (although I've read a LOT of poor reviews on it). The only issue I've seen is it can definitely produce some strange bokeh effects.
Exhibit A: this shot at 400mm f/5.6 iso100 (the 70-200 with the 2x)
Just to be clear: a 1.4x teleconverter will make your max. aperture one stop smaller, and a 2x teleconverter will make the max. aperture 2 stops smaller. So on your 70-200, that means 2.8 becomes 4.0 and 5.6, respectively.
I have a 2x that I use with a Canon EF 100-400mm f/4.5-5.6L IS. At 800mm not having auto focus was a real disappointment with my 20D. Everything got much easier with the 40D and live view.
