Would the different cycles of universe in the Conformal Cyclic Cosmology Theory be the same?

There is no reason to suppose that they would be the same.

The theory's main proponent, Roger Penrose, hopes that some "echo" of the previous cycle might be present as faint cosmic rings, present in the distribution of mass/energy across the sky. There is some modest evidence to support the existence of such rings, less to link them to CCC. The expectation is that the distribution and exact locations of these rings would be arbitrary, and thus would differ from one cycle to the next.

The expectation for all other macroscopic phenomena is the same.