If money is no object then by all means the 200L IS.
And if money is an object and you like that length, you might give the 200L non-IS a close look. IQ wise, it's basically the long end of the 70-200L IS2 but with better bokeh.
Plus it's compact, light, black, has as good or better AF. Also pairs with the Canon 1.4x TC as well as the 70-200 does. And it's inexpensive.
IMO, about the only dowwnside is that 200 and longer is a bear to shoot without IS, tripod, whatever unless its light enough to take the shutter speed way up.
Test shot of bird on a wire, ~70% crop:
 Shot raw, no contrast, color sat, local contrast added in post. Only moderate sharpening and "hdr" added to bring out a bit more detail in the shadows and tame highlights. So hopefully this is a decent representation of what to expect from this lens.