According to the Litigation Lobby, limits on damages (like those in California's MICRA statute) have no great effect on the sums doctors must pay to insure themselves against liability claims. Here are some actual numbers on the differences, from the Orange County Register, and using premium data from the Doctor's Company (via KevinMD).

Neurosurgery:

LA/Orange Counties, Calif., $83,000
Miami, $369,000
Chicago, $330,000
Las Vegas, $275,000

Obstetrics and gynecological surgery
LA/Orange Counties, Calif., $63,000
Miami, $248,000
Chicago, $221,000
Las Vegas, $219,000

For claims that the insurer-bashing Proposition 103 deserves credit for the low California rates, incidentally, see this post and this one ("about half of medical liability coverage in California is provided by entities that aren't even subject to Prop 103; and the measure's provisions requiring hearings following challenges of any rate increases above 15 percent have seldom kicked in because insurers haven't mostly pursued rate increases that high.")