Hilsea will allow you to clearly see every train that passes onto Portsea Island. So will Fratton but it's busier and you have more chance of your shots being ruined somewhat by other people.
Typically, each hour at Hilsea, you'll see eight to ten South Western services, six Southern services and two Great Western services pass through.
Bedhampton (one stop up from Hilsea on the Portsmouth Direct Line) is also quiet with plenty passing through. You won't be able to see the Great Western service and there will be less South Western, but instead you'll see far more Southern trains as the Southampton services run through.
Typically, each hour at Bedhampton, you'll see four to six South Western services and ten Southern services pass through.
Worth nothing the vast majority of Southern services now terminate at Portsmouth & Southsea, so Portsmouth Harbour is not the ideal station to see these.