Specific surface is basic parameter. You can obtain it from producer or you can measure it by BET method. There is possibility to calculate the specific surface also. You have to know inner structure of nano-structured powder particles for this calculation.
Be carreful about method of production and the quality of carbon materials, there is of course the general rule of surface area to volume ratio but never forget that for instance the CNT synthesized by HiPco are much more fragile than those made by laser ablation for instance. I suggest you to experience!
I think CNT will be more sensitive. Graphite edge planes having more effective capacitative behavior than the basal planes. For reference you can go through the following link
want to say with Guillaume, suggest you to experience
Graphene would be more sensitive primarily because two surface areas directly come into contact. In case of CNTs the outer surface is ok, but you are not sure about the inner surface.
It would be graphene because of its direct contact and tremendous active surface area! For CNT, Dr. Vijay Jindal is right about the inner surface issue with the CNT.
In the case of hetero atom doped reduced graphene oxide one has to take into account of the defects which inhibit conductivity although they possess high surface area. In the case of carbon nano tubes one can selectively functionalise the outer surface by not modifying graphitic interior this can enhance the conductivity of the carbon nanotubes when compared to graphene based materials. A hybrid consisting of both graphene and carbon nanotubes can be more appropriate choice as it combines both high surface area and conductivity.