Cosmology is more detailed and thorough than Modern Cosmology, although the structures of the two books are roughly the same, i. e. start from the smooth universe to the perturbations. I particularly enjoyed the derivations of fundamental equations for perturbation and temperature fluctuation in Cosmology which is clearer than Modern Cosmology. However, Cosmology does involve massive and complicated calculations. You could easily get lost in long equations if not following the main ideas and it takes time if you actually want to check all these calculations.
In general, I would say Modern Cosmology is more friendly for the first learners and one can grab the basic concepts fairly quickly without worrying about losing too many details. Also latest edition of Modern Cosmology might be more updated than Cosmology. On the other hand, I highly recommend Cosmology for advanced learners for it gives you more insight into this subject.