See my nickname, DS1 started state school today, so my opinion fairly obvious as well...
I am sure only children are no worse off than children with siblings, but IMO their upbringing inevitavely (sp??) will be quite different. I watch my DSs 1 and 2 and am quite certain that NO entertainment I could offer would give them as much fun, pleasure and excitement as playing with each other (oh yes, and fighting...).
As fas as not loving a further child as much as the first: love is not a finite commodity, the more you have to love, the more love you will have - does that make any sense without being too sugary-sweet?
Jealousy: yes, occasionally somebody's nose is out of joint because of perceived slights. Well, that's a life lesson, is it not: life is not always fair, sometimes other people have something oneself has not etc.
DS1 and 2 a lovely big brothers to DS3 aged 5 months: they play with him and make funny faces to make him laugh, then ignore him completely, NO jealousy at all. We had said to them when I was still pregnant that new babies are really quite boring, cannot do anything for themselves, will need mummy and awful lot just like they did when they were little. We did not constantly say (like some well meaning family members and neighbours): how exciting, you are going to have a new baby, somebody to play with etc.
So, bottome line, a resounding vote for the sibling. Private schools are all very well, but a bright child will do well at state schools and a child which may need extra support a lot of private schools are not interested in because they "spoil" the league table.
Do what feels right to you and DH.