First, I think, there's no reason to choose one or the other. I can like both and depending on my mood, I'd favor one over the other. Still, it's music to be enjoyed and creating a comparison kinda leaves behind the idea that it is ok to have different musical flavors.
I will, however, point out that suggesting The Beatles were less sophisticated than the Stones is on odd point to make. The Beatles were regularly messing with time signatures (Here Comes the Sun, Strawberry Fields) and a variety of of orchestrations.
This isn't to say anything negative about the Stones in as much as the comparison is an odd one and the reasons seem much more personal than based on what is really true in each artist's catalog.
