Actually, the Department for Transport considers both Newhaven and Shoreham to be Major ports for commerce, and Newhaven a Major port for passengers.
Vehicles using Newhaven ferry went from 123,000 in 2014 to 175,000 in 2016.
Having lived in both... they're very hard to compare as Brighton (and I think we should talk about the urban area here) is spread along the coast. So when you say from one side to the other, do you mean from Saltdean to Littlehampton or do you mean from Shoreham beach to Shoreham airport...