You take a big IQ hit with the doubler. I rarely use it (2XIII) anymore except on my 70-200 2.8L IS II. I find I can crop without it and get better IQ. I believe the added "feature" is not worth all of the hype. Might prove useful with the video folks where the loss if IQ is also lost in the downscale to HD. For stills, cropping is still better than using the 2XIII.
Depends on the lens. The 2x III is MUCH better than upscaling from a bare a 300 2.8 IS or 300 2.8 IS + 1.4x TC III. At first I was all oh no my 300 2.8 IS looks like a tamron 70-300 vc now when I used the 2x TC but I learned to get over that since in the end you put so much more detail on birds and such that when compared in a fair way you see the 2x does so much so it's almost permanently locked on my 300 now for birds (even often enough for surfing, but basically never for soccer or football) unless I am in a close blind or something.
It even brings a bit more detail on a 70-200 f/4 IS than upscaling (compared to bare lens or with 1.4x TC III on)! Although the image does suffer in some ways that makes me think it is not worth it so much in that case despite a tiny bit more extra detail.
The 70-300L definitely does better with the 1.4x TC III than upscaling, not even close. Just hope they enable the AF like they did, unofficially, for the 1DX!!