> How is this different from CI but with probability of observing given state - which was also determined empirically?
It's not different, that's the point. For both interpretations, the relationship between the probability of observing a certain outcome and the amplitude of that outcome in the wave function are an extra postulate, the exact same extra postulate in fact, the Born rule.
> The worlds and their number are equivalent to the states & probability of CI without having to introduce the "measurement apparatus" that is distinct from the quantum system.
The measurement apparatus as a separate thing from the quantum system was actually partially explained by decoherence (ironically discovered by MWI proponents), which needs this separation for the same reasons as CI: we need some way to explain why quantum phenomena don't happen at our scale. Now, MWI makes this concept relative to an observer, whereas in CI it is often assumed to be absolute.
Basically, we can deduce from the Schrodinger equation alone that after the interaction of a quantum system with the environment, coherence is lost, and the different "states" of the wavefunction can no longer interfere with each other.
CI postulates that, as a result of this interaction, only one of the states will remain, with the Born rule probability. This is the most direct way of interpreting our experimental results.
MWI says that nothing changes after this interaction. It postulates though that, if we were to ask how likely we are to be in the same "state" as a particular result, we should expect that to be the Born rule probability. This explanation takes the theoretical description of the wave function to be more real in some sense than the actual observations we make.