D700, particularly if that includes indoor hockey.

Basically, indoor sports are the most demanding because they need fast shutter-speeds in low-light, so they need to perform very well at high ISO. Not only are full-frame models usually better for that but the D700 is an awesome low-light performer because it has large pixels even for a full-frame camera.

As you suppose you guessed it, having fast lenses helps too. Stabilization is not really needed when shooting sport action since you need a fast shutter-speed anyway, so that can save you money.

The lack of a 100% coverage viewfinder is the reason I would NEVER buy a D700. It's a killer for me but its a personal choice. However, it is much less relevant for sports where action is moving so fast that you have to frame generously to keep the subject under a focus point and then crop later. Once you have to crop, well, you have to crop. Frankly I think it was embarassing for Nikon to have 100% OVF in the D7000 and not the D700 and they corrected that in their models. Yesterday I got a Nikon D600 which - despite the lower number - is extremely good.

You are also right about the crop-factor. An 70-200mm on an APS-C sensor body is very suitable for hockey and you could go with the same for full-frame but your shots wont be as tight when players are away from you. If you are an official photographer, you can get closer or get a longer lens but you will lose a stop unless you have a big budget. Something like a Sigma 100-300mm F/4 which is ultra-sharp is a fantastic option.