You can contribute $18.5k to both a 403b and to a 457, if your income allows of course. A total of 37k tax advantaged space.
If you investment options are the exact same in the 403b and 457, and you will get the 403b match regardless of contributing to it, then it is smarter to max out the 457 first. The reason is that 457 allows you to withdraw from it, without penalty, the moment you separate from the university (retirement, find a new job, quit, or otherwise). There is no age minimum for penalty free withdrawals.
The reason someone may want to contribute to a 403b first are: 1) investment options in the 457 are bad or have higher fees, 2) need to make contribution to 403b to get a match.