Both are very mixed towns (I grew up in a village in between them), some nice parts, some distinctly not so nice parts to both of them. I can't say much about schools as I moved away long before we had children, however you can live in a nice part but be in the catchment area for schools in the not so nice parts quite easily, so take care. Bedhampton/Drayton/Farlington/Cosham run in a line between Havant and Portsmouth and are all reasonable areas, Fareham is nice, Purbrook and Denmead are also ok heading back up towards Waterlooville. If you are prepared to go a bit further, Emsworth is very nice, Rowlands Castle is nice (v. near Havant), both are more separate than the other areas I have mentioned. Horndean is ok too.
Havant and Waterlooville are both medium sized towns but they aren't particularly special town centres (not bad, but nothing special). The area is quite built up, all the towns and villages sort of run into one another so the town centres suffer a bit through competition with each other and nearby Portsmouth.
One big difference is that Havant has a mainline train station with trains to London, Portsmouth, Chichester, presumably Southampton too, whereas Waterlooville/Purbrook/Denmead/Horndean are not on the railway.
As for pre-schools, there are few state funded ones here, but all children receive some funding (15 hours I think) from age 3. Some pre-schools take from age 2 but you pay the full fee. For under 1s or full day childcare you would need a nursery instead (3 year would still get funding for that). Some nursery/pre-schools are attached to infants schools, most are not.
Actually, I do know a bit about secondary schools in the area, Springfield in Drayton has a good reputation but is very popular, also there is a Catholic school in Waterlooville which has always had a good reputation. You would need to verify all this though as I am possibly not up to date.
PM me if you have any more specific questions.
Oh, you might find the local newspaper helpful
News if you click on its News button there is a section for each local area including H/W.