Not exactly. If you use the same soul as your last character what you retain is skill ramps, this allows you to reach the same level you were before much quicker. In turn that allows you to actually become more powerful in the next life. You will not necessarily start from zero skill either as your character will have learnt skills during their childhood based of their parents and region.
So no, you do not just keep the same skill level, but your previous life dramatically impacts your skills this life and allows you to continue to advance.