Many people are of the opinion that East Dulwich is nicer than Forest Hill. It has some great local private schools, Dulwich Park and Dulwich Picture Gallery are both not too far away. The high street has lots of gastropubs and nice food shops (cheese shop, organic butcher, fishmonger, etc) - all the things that we would love to see in Forest Hill.
But there is a downside to East Dulwich - it has ONLY gastropubs, and trains only go to London Bridge, while Forest Hill trains will shortly go to three central London destinations - London Bridge, Victoria, and Shoreditch. Also whilst their pool is being refurbished, ours is being rebuilt behind the existing facade.
East Dulwich is currently more expensive than Forest Hill, but don't count on this lasting for ever! Forest Hill has been undervalued for years but there is enough infrastucture investment that this may start to change between 2010 (Overground trains) and 2015 (Thameslink trains providing direct links to Kings Cross).
If you would prefer to pay less for your house, value transport links, and are not currently thinking about private education - you will probably be very happy in Forest Hill.