My purchase order has been:
70-200 f/4L IS > 85 f/1.2L II > 200 f/2L IS > 70-200 f/2.8L IS II
I purchased the 70-200 f/2.8L IS II because I was sick of lugging around the 200L when hiking etc.
But the f/2.8L IS II is a far closer lens to the f/4L IS than it is to the 200L - so now I still carry around the 200L when hiking in addition to the f/2.8L IS II
(Basically I think the 70-200 f/2.8L IS II is a jack of all trades but master of none)