I get that the f/2.8 will bring more bokeh effect to it than the f/4, which is nice, but for the lower light situations, will f/2.8 beat the IS function at f/4 when handheld? The price difference between the two is huge, so there have to be more to it.
The question of IS vs. wider aperture depends upon your subject matter and camera stabilization.
- If your subjects are moving IS doesn't do anything to prevent motion blur at slow shutter speeds. The faster shutter speed allowed by the wider aperture of the f/2.8 lens will be more useful.
- If your camera is mounted on a tripod IS is redundant.
- If you are shooting stationary subjects while handholding the camera IS will allow you to use up to 3-4 stops slower shutter times (compared to shooting without IS) before blur from camera motion begins to be noticeable.
As far as depth-of-field goes, f/2.8 vs. f/4 is just another option that one lens offers and the other doesn't. Sometimes that difference can be the difference between getting the shot you want and the shot for which you have to settle. How much that is worth to you is an individual decision.
Beyond those obvious differences there are the overall optical qualities of the two lenses.
- Some tests have found the EF 24-70mm f/2.8 L II is sharper at f/2.8 than the EF 24-70mm f/4 L IS is at f/4! When tested at the same apertures as the EF 24-70mm f/4 L IS the EF 24-70mm f/2.8 L II is clearly the superior at all common focal lengths and apertures. As is the case with most lens comparisons, as both lenses are stopped down the differences narrow and by f/8 there is little difference between these two lenses. The f/2.8 is a sharper lens than the f/4, especially in the middle of the focal length range around 50mm where the f/4 is at its weakest. Whether the f/4 lens is sharp enough at a significantly lower price is an individual decision.
- In terms of Minimum Focus Distance and Maximum Magnification the EF 24-70mm f/4 is more useful. It has a Macro mode with an MFD spec of only 7.9" that yields an MM of 0.7X. In comparison the EF 24-70mm f/2.8 L II has an MFD of 15" and an MM of 0.21X which is more typical of a normal zoom.
In the end, asking if the premium price is worth it comes down to how you plan to use the lens. If you're shooting moving subjects in low light the EF 24-70mm f/2.8 L II is the better lens and can get shots the other lens can't. If you're shooting landscapes at f/8 from a tripod both lenses perform about the same and the EF 24-70mm f/4 IS is a better value. If you need to shoot subjects close up at near 1:1 macro magnification then the EF 24-70mm f/4 offers utility that the other lens lacks.
The IS will allow you to handhold the lens at a much lower shutter speed using the stablisation to compensate.
However in times when you want to use a faster shutter speed, e.g. event photography where people are moving around, the 2.8 will give you a stop more light to play with which IS will give you no benefit from.
Of course you can just increase ISO, but you do get the noise increase too.
(Side note: it's a genuine shame Canon don't do a 2.8 IS 24-70, as with the 17-55 the IS DOES make a difference)