For what it's worth, I'm pretty happy with the 24-70 4L IS for my purposes. I like its combination of relatively small size, light weight, and IS. And for someone like me who does not do enough macro to warrant buying a true macro lens, the macro mode can be a bit of fun. I particularly like it as a lens for hiking (especially when doing multi-day hikes with people who are not that interested in photography, which makes travelling light particularly important to me) - it works well as a landscape lens, the macro mode can be useful for little things you come across along the way, and it does fine for some portraits as long as you aren't looking for shallow depth of field. I've also been pleasantly surprised by how how useful I've found the lens indoors, with the IS counter-acting the comparatively slow max aperture, although of course the IS is not relevant when you want to stop action.
Regarding sharpness, there are a number of negative reports about the 24-70 4L IS, but also some very good reports (eg SLR Lounge) if you look around and it seems possible there is quite a bit of sample variation out there. Lens Rentals has an article about how complicated the lens is internally, which might explain why there are more than a few which are not well tuned (as pointed out to me previously by another CR member). If that is the case, some of the poorer samples presumably would be dragging down the average scores reported by LensRentals, which still have the 24-70 4L IS in second place behind the 24-70 2.8L II for sharpness amongst the 24-70s (albeit the Tamon 24-70 2.8 VC almost ties with it). From my own experience, my 24-70 4L IS was very poor at 50mm when I got it, but I had it serviced by Canon and it's a world apart now.
I am not trying to talk you out of the 24-70 2.8L II, and I'm not suggesting the people recommending it are wrong to recommend it. By all reports it's fantastic, but only you can decide which lens best suits your needs (and budget). It all comes down to what you want to use the lens for and your personal preferences (including about things like size and weight), so I'm just trying to give you a different viewpoint in case it helps you think through your decision.
You mention having IS might be useful to you for video, but you also mention bokeh. Obviously a 24-70 2.8 (whatever brand) will allow shallower depth of field, which should translate to more blur, which is often associated with "better" bokeh. My suggestion, then, is to think about your lens kit overall. If I had only one lens covering 24-70, I would choose the 24-70 2.8L II over the 4L provided I could afford it - in short, aperture would rule for me. However, if you really like bokeh and you are happy to own a few lenses, you might want to look into a prime or two so you get significantly shallower DOF (and probably "better" bokeh), and an even greater ability to stop action in low light, than the 2.8L II would give you. And if you go down the prime lens route, you might prefer a 24-70 4L IS in your kit over the 2.8L II so you have the IS for video plus save some money (amongst other potential reasons).
Whichever lens you end up getting, I hope you enjoy it!