Howdy
I live in the new forest slap bang in between bournemouth and southampton and go to both on a fairly regular basis.
Generally as a city I prefer southampton, Shopping is a lot better there than bournemouth, all the good shops are close together and west quay is there which is a pretty massive shopping centre.
The shops in bournemouth are really spread out, like everything else in the town. Although I would say the main advantage of bournemouth is that it is a lot less 'city like' there is a nice big landscaped park in the centre of town where all the students go to laze about in the summer.
Southampton has some really rough areas which I wouldnt go anywhere near when the sun goes down. I would feel a lot safer walking through bournemouth at night than I would in southampton.
As far as clubbing is concerned Id say they are pretty much on par. Bournemouth's clubs, like the shops, are fairly spread out but If you dont mind a walk between clubs then there are quite a few good clubs, especially in the summer when the city really starts to get busy (It a a tourist town after all).
Southamptons clubs are a lot closer together so not so much walking around. But both the cities have a similar range of clubs. I tend to go to southampton more for gigs and clubbing more in bournemouth... dunno why, Just seem to have had better nights out in bournemouth. There is also a lot more smaller 'bars' to go to if you dont feel like a really messy night and just feel like a quiet drink.
So for shopping, transport, gigs and things like cinema etc I would go for southampton.
For clubbing, and having more of a studenty vibe I would go for bournemouth.