A couple of things I know:
It is incredibly rare for personal assets to become subject to judgement in standard malpractice settlements. (Can anyone find a SINGLE example to the contrary?)
Having said that, 401ks and IRAs are more secure than 403bs (which are usually the account offered by the hospital--because they are a non-profit organization.) 403b's factor into many financial situations in slightly different ways than 401ks. Unless you are getting matching dollars from the institution, it is probably wisest to put any money you have into a Roth IRA or a traditional IRA.
Your lawyer will be upfront with you, in the case of a suit, about how much the max payout will be (after reduced by ?appelate, which jackpot settlements usually are) and should advise you where your insurance leaves you exposed--if it does. Lawsuits churn for years, it seems that there is plenty of time to establish these things, if necessary.