I will echo Erik's statement about CF tripods - I'm really not too sure about its utility against heavier tripods - or maybe I'm spoilt coming from the video world. I've used light Gitzo CF, and I found them almost 'toy-like'.
Ahh... you meant if carbon is better than say a heavy aluminum tripod? Stability is certainly the main factor, an alu tripod that can support 40 kgs is certainly better than a carbon that can support 18 kg. However, a carbon tripod can be made lighter than an alu tripod with the same stability, that is the advantage for us that carry the equipment out in the landscape.
I've heard that carbon legs have better properties concerning damping vibrations introduced from the ground or the wind compared to aluminium, but I don't know if that is true, perhaps there is a little difference. I would guess that wood could be better than aluminium in the same way, but then we get really heavy tripods. My reason for using carbon is being able to have an "overkill" stability without carrying too much weight.
I use a Gitzo GT3541XLS Systematic (max load 18 kg, my equipment weighs 3 - 4 kgs). It has a max height of 6.6' (198 cm) despite having no center column so often I use only two of the four leg sections, and sometimes do overhead shots, it only weighs 2 kgs (4.3 lbs). I think one should go for the more robust carbon tripods, the smaller lighter Gitzos are indeed a bit toy-like. The drawback of this tripod is that it kind of sucks for macro shoots near ground level, but I can manage.