Canon 200mm F2.8 L > 70-200 F4 L IS?

Hey guys. I currently have the 200 2.8 L and really like it, but I am finding it quite limiting in its use. This winter it has been really hard to find decent enough weather (in London) to be able to use it without high ISOs. I am using it for candid street / outdoor portraits / motorsport etc. I have started looking at reviews of the 70-200 F4 L IS which are making me think if it would be an upgrade or if I'd lose out too much in the Bokeh and qualities of the 2.8? Or does the IS make the F4 more usable than a 2.8 without IS?
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