I've visited both, so here goes:
Southampton:
1. Overall, an academically strong university - I think the Economics dept. is of similar standard to Exeter.
2. It's distanced from the city centre so it is bus-linked everywhere.
3. Good night life.
4. Nice modern campus
5. Near to the New Forest
Exeter:
1. Like Soton, its a decent uni so no worries there.
2. Very green, attractive, cosey campus.
3. Crud nightlife, and apparently a poor students union.
4. Over representative of the white, middle-class. This is only a problem if you make it one, but there is no denying the fact that Exeter is pretty "posh", despite what people try to say - stereotypes arise from somewhere at the end of the day.
5. In a very nice part of the country, safe city, small and compact...
6. Close to the city centre.
Overall, I would say pick Southampton. Academically there is little difference between the two, other than the fact that Soton is generally perceived as being more research-intensive than Exeter.
But I think Soton is better in the sense that there is more to do, and the student composition is more mixed. I think you need to look at the courses and definately visit Exeter. It really has a gorgeous campus and you may well love the idea of spending 3 years there.