Portsmouth a mixed bag - agree with PP that there is a lot for teenagers and Southsea, Gunwharf Quays, Old Portsmouth areas all lovely. Theatres, cinema etc all great and there is a very wide range of places to eat.
The Historic Dockyard is fabulous and there is a good mix of housing across the city but there is significant deprivation too. The main city centre (Commercial Road) is getting increasingly run down - the large M&S there has just closed with the clothing and food halls relocating to edge of city retail parks.
If schools are relevant to you then look at the OFSTEDs and other info as some of the schools are really struggling and a very recent report on the BBC said that Portsmouth schools have some of the poorest results in the country. That said, I have friends whose DC are in secondary schools there and they are happy with the education their children are getting. If the independent schools sector is your thing, Portsmouth High School for Girls and the mixed Portsmouth Grammar School have outstanding results.
Chichester is lovely and the range of shops etc is outstanding. We are in Portsmouth for work reasons and we and our DC really enjoy being there, particularly the wonderful walks along the sea wall bounding Old Portsmouth but if we had a choice, would probably prefer to live in Chichester. That said, my DS who is at Uni elsewhere likes Pompey so much that he and his GF are planning to try and get jobs here once they graduate.
There are some fantastic Georgian and Victorian properties which are considerably less costly than their equivalent in Chichester. Traffic in and out in the rush hours is dreadful and I loathe the A27. But I do love that the Isle of Wight is so close at hand and that we can see the cross-Channel ferries and the Royal Navy ships coming in and out of the port from our window. We are so close we can wave at the people on the decks of the ferries which is lovely.
We've been here two years and are relocating abroad with work next year but will miss it when we go. That said, we are bound for Herefordshire once we return to the UK because that's where our hearts lie.