It's not a $150 price difference for the camera; the price difference for just the camera is $50 ($500 vs. $450), and the lens is the rest of the price difference ($650 vs $500), so a quick breakdown:
Camera:
The D3300 has better software and a new carbon/polycarbonate monocoque construction, and a modestly better ISO capability, and will handle faster and with newer more intuitive menus. Also, you'll have firmware upgrades and support for a longer period of time than on the D3200.
Lens:
The 55-200 lens that comes with the D3200 bundle lacks any image stabilization, and is an old design whose main benefit is that it's cheap, and you can see that as you're only paying $50 in the bundle for it. The 55-200 VR II lens that comes with the D3300 bundle has image stabilization, a collapsible lens barrel, and has much better technical image quality and is actually constructed better so it'll hold up to more. You're paying $150 in the bundle for it, and it's worth it.
Overall, I'd say spend the money if you can afford it, the investment will more than pay off over the life of the camera, particularly as the money is going to a better lens, not really the body itself.