I'm not quite sure what all the fuss is about the 24-105L.
On a FF body it's ok (at a stretch), but is an L lens in name only. It's totally outclassed by the 17-55 f2.8 (which is better in all regards except in reach). The Sigma and Tamron equivalents are just as good to the eye as the Canon 2.8 (especially so given the low resolution of HD video compared to stills), albeit with slower AF, but again this doesnt really matter for vid of course. The Sigma and Tamrons are also about a quarter of the price.
On a crop body the 24-105 give us an equivalent focal length of about 39-160mm, wheras the 17-55 gives you 27-88mm equiv. Which focal lengths are more usefull to the OP?
A crop body already has double the DoF of a FF body (at a given aperture), so sticking an f4 lens on it will look far less 'cinematic' than a f2.8, and of course we would need to ramp up the ISO to match the exposure too when trying to shoot wide open.
So, the L lens loses out on IQ, IS, wide angle capability, aperture (DoF, noise, 'look'), and gains only in reach (but does the OP really need that with the 3x zoom capability anyway?). I guess we get to wave our red ring about proudly though.
Obv it will come down to what the OP wishes to shoot, but 9/10 cats ignore the L stamp and go with a 17-50/55 2.8.
Dammit, thats 4p of mine so far, and I've not even posted an introduction in the Noobs forum!