We like both of these properties the best of all the WDW locations. We have very similar family situations. We have 3 kids as well - DS9, DS7, and DD3. We were just there June '04 and couldn't decide on which resort, so we stayed 3 nights at BCV and 4 nights at VWL (and 5 at VB as well!). That way, we could focus on EPCOT and MGM the nights we were in BCV, and MK the nights we were in VWL. We also had my parents with us, and we wanted to show them as much of
DVC as possible - it must have impressed them, as they gave us enough money to go buy 150 points at HH as soon as we got back from vacationing with them!
TeresaNJ summed up very well the differences between the 2 resorts. If I had to absolutely pick one, it would be VWL, but I'm also swayed for sentimental reasons. WL was the first WDW resort we stayed in as adults, AND the first resort we stayed in when we took our kids for the first time. Little did we know what we were getting into!
For us, the ultimate "Welcome Home" is grabbing a cup of coffee, running to the dock, and taking the boat from VWL to MK in the morning for early entry when the sun is just coming up over the lagoon and the mist is still in the air. It don't get much better than that!
Seriously, if you can't decide, consider switching halfway through. The CMs make it as painless as possible when moving. They come get your stuff, store it while you check out and hit the parks, and have it waiting for you at your next resort when you check in. They'll even store your refrigerated food for you in a big walk-in fridge.
As far as heat and crowds go, June is 'transitional'. Early June is still OK, as the schools in the Northeast aren't out yet (we're in Kansas and get out before Memorial Day). By late June the crowds are in full swing and it is starting to get warm. Drink lots of water and always have a water bottle in the parks to fill up, especially for the kids. Soda dehydrates them with the caffeine.