Depends if you want a great focal range or a greater aperture. One is not better than the other, it entirely depends on what the user wants from it.
Hi Ali -- fair point. In this instance, I am interested only about lens performance between the two. I have read their respective reviews on photozone.de as well as looked at them on the DXOMARK site. Seem to have good performance for a zoom, but not as steller as say the 17-55 is viewed on Canon APS-C sensors.
There's really not going to be much real-world IQ difference between the two lenses. The only thing that might cause an occasional issue is the field curvature of the 24-70mm. Also, I'm not convinced that's the right approach. If you need f/2.8 for a 1-stop shutter speed advantage in order to stop motion, a slightly less-sharp lens at f/2.8 will produce better results than a slightly sharper f/4 lens that gives you subject motion blur. With indoor ambient light shooting, overcoming subject motion can be a struggle.
It really does come down to aperture vs. focal length. I do find that with the 24-105mm f/4L IS, I often need a flash to shoot my daughters indoors. But my experience with the 70-200mm f/2.8L IS II suggests that sometimes just the one extra stop is not enough - I often use the 35mm f/1.4L for indoor shooting with ambient light.
One other consideration is the amount of OOF blur, which will be greater with the f/2.8 lens. If your daughter is anything like my two (ages 2 and 4), your family shooting 'around the house' will probably be against a certain level of background clutter. An f/2.8 lens can render that clutter as a pleasing, colorful blur.
I do think that for a travel/general use lens, the 24-105mm f/4L IS is a better choice. But I have been quite tempted by the 24-70mm f/2.8L, as I often find myself switching to the 70-200/2.8 II and using it at 70mm in the house.