I presume you mean Gatwick to the hotel which is close to Old Steine?
From experience you will hit a few slow-traffic points when you first come into Brighton from the north and when in the actual center. The taxi will have the advantage of being able to use the bus lanes though, this will be...
My suggestion is to get a taxi from the airport to your hotel. This will remove all the time needed to get to the train station, buy a ticket, wait for a train and get from the station to the hotel at the other end. Taxis are quick to get in my experience.
I presume you can use the e-gate...