My totally unbiased opinions:
Heavy/big/bulky lenses: advantage f4L IS
The sharpest zoom Canon (and for that matter anyone) makes: advantage f4L IS
Handholding at 1/5th sec: advantage f4L IS
I owned a 70-200 f2.8 L non IS for over a year and I can count the number of shots at f2.8 I took on the fingers of one hand but like Walt says if you know you're going to need f2.8 a lot then there's not much discussion.
The only thing you mentioned above that would make me seriously consider the f2.8 is weddings as an f2.8 lens is going to give better BG blur when you're in portrait type shoots. However the f2.8L IS is the bokeh king not the straight f2.8.
I still maintain you can pretty much do everything you need to with f4 and unless you absolutely know why you need f2.8 you'll be happier with the f4' versatility.
I have owned all the Canon 70-200's (the straight f4 twice) and I will never sell my f4L IS, I'd just add an f2.8 if I really needed it.
One more thing to think about
: you'll get on average more keepers with IS at any focal length and at any shutter speed. Whether anyone thinks there is the potential or not camera shake is always possible, heck I see it all the time with my 400 f5.6L even at 4000th sec.
Anyhow you can't go that far wrong with either, they are both great lenses.