For me to say I live in "Sussex" has always been instinct and practice. I guess it depends on age, and a bit maybe on sporting interests, but presumably there are plenty of people who do use the "East" and "West"...? We could have a poll of NSCers...?
I think I us both. I often say I was born in Sussex, but will also say, from Portslade, Brighton, East Sussex, as that was part of the postal address.