Here is my progress: We basically need to find which compound has more single bond character. Now both compounds will break the double bond, and give the electron pair so as to make both cycles aromatic. But what do I do after that?
Cleavage of the double bond will lead to both compounds having two rings that are aromatic, however the amount of resonance energy(hence stability) will not be the same.
Both systems will have a Cyclopentadienyl anion, but one will have a Cyclopropenium cation while the other has a Tropylium cation . As the Tropylium cation has more resonance structures, it will have a higher resonance energy and hence greater stability than the Cyclopropenium cation. So (b) has a lower bond rotation energy.