I guess that's fairly subjective and would depend on the distances to and between your subject and the background. But I can say that I've taken plenty of tight portrait shots with my 24-105 f4 at 105mm/f4 and I've been happy with the amount of background blur, and the 70-200 f4 is even better. The 70-200 f2.8 is an absolutely awesome lens though and if I had the money to spare I would buy it.
EDIT: also if you don't need the length but desire nice bg blur then what about a 50mm f1.8/1.4/1.2 (depending on budget)?
It will depend on distance to subject and then to background. One of the reasons we used to use mild telephoto lens for portraiture was so that we stood back a bit and then the lesser depth of field of the telephoto took care of the background.
The older lens's used to have depth of field scales on the barrel and depth of field preview buttons that stopped the lens down so that you could see the effect in the viewfinder.
I once did a test between F2.8 and F4 trying to decide between a Nikon 70-200 F2.8 or the newer F4.
There wasn't a lot of difference in background blur and either will produce it.
F2.8 is good for indoors but then in the case of Nikon the F4 version had a later version of vibration reduction.
Also with excellent high ISO low noise performance the need for F2.8 for indoors is less. Between excellent high ISO performance and low high ISO noise there is even less need for F2.8. Savings in cost, weight and size add to the advantage.
However after having said all that I do like F2.8 lenses a lot. If you were going to use it for astrophotography F2.8 is important. F4 really requires tracking.
for this you simply have to do lens test as different lens with the same spec will have different bokeh. I think it is cause by the shape of the aperture blades and mainly shows up in highlights in the background such as sunlight reflected off foliage.
F4 will allow decent background blur particularly at longer focal lengths, perspective is changed though. The longer the focal length the flatter the perspective.
If you're taking portrait shots for example at 35mm f2.8 and one shot at 100mm F4 you may have the same background blur but the perspective of the subject will differ. If you're not sure try and find a hire place and hire both an F4 and F2.8 for a day.
The 70-200 f2.8L is a heavy beast of a lens, the F4L is very light in comparison.