Hi,
I think the major differences are:
*in classical mechanics we deal with no uncertainty, everything is fully determined and exactly determined by the laws.
Also, particles are only particles and waves are only waves, they cannot have dual aspects.
*while in quantum world , we just talk about probability amplitudes , or probablility to have a certain particles at certain position, there is uncertainty in everything.
Also, particles can behave as waves -> they can interfere (Actually this means that their probablity interfere destructively or constructively to have no particles at certain locations and many partciles at others,and inversly waves can behave as particles as in photoelectric effect.
Refards,