Both sentences are correct. (The second one should be, though, "I'm being much better paid than before.")
Both sentences refer to the fact that now, you are making more money than previously. In A) there is slightly more emphasis that the condition of your being paid much better is of a more permanent nature. In B), the emphasis is on the possibly temporary nature of your being paid.
However, the sentences could be used interchangeably in sentences like the ones you posted.
Maybe a conversation would go like this:
A: How's the new job going?
B: Can't complain. I'm much better paid/ being much better paid than before.
A: Think you'll stay at this job?
B: Maybe. Unless I find an even better job where I'll be paid even more. Then I'll move on again.