re: What’s are the differences between a 403(B) and 457(B) retirement plan?

Assuming the match amount and the vesting schedule are the same, there aren't too many functional differences. 457b's allow for larger catch-up contributions to be made when you're nearing retirement age and withdrawals from
457b's will not have early withdrawal penalties assessed for cash distributions taken prior to 59 1/2. They should operate relatively similar otherwise.

Main thing I'd probably look at is the investment offerings for both plans. One may have access to some funds that the other doesn't, or that you just prefer.

It also may behoove you to check out in-service distribution options for both plans. Plans can choose to allow(or not allow) a couple of different in-service distribution options. If having some level of access to the funds pre-retirement is important to you, then you may want to check and see what distributions are allowed and factor that into your decision.