Hardware differences in the 4GB Xbox and 250GB Xbox?
Solution 1:
First, realize that, among other things, your old drive will not work in the new 360 Slim, so you would need to find one of the old models in order to keep your harddrive. If you do happen upon the old design, the second thing you should realize is that a lot of the downloaded content on your harddrive is keyed to your current console. There are ways around it, but it isn't as straight forward as plugging your old harddrive into your new console. Note that this method should also work with the new slim models.
As for the differences between the 4GB and 250GB models, the 4GB model is pretty analogous to the old Arcade models. It comes with an empty harddrive bay, which accepts the same style harddrive as the 250GB model. Some games may not allow all of the features for the 4GB consoles, although this may have been fixed. As far as I know, the rest of the hardware is the same. You could just buy the harddrive to put in a 4GB console, but that's paying an unnecessary premium. Personally, I would get the 250GB slim model if I were forced to replace my console at my cost.
Solution 2:
According to the Wikipedia article, it appears the 4GB model and the 250GB model contain the same hardware. However, there was a cosmetic difference - the 250GB model had a glossy finish whereas the 4GB model has a matte finish. They both now have a matte finish (starting in August 2011). Also, the 250GB model comes bundled with a wired headset.
Solution 3:
The 4GB version has onboard 4GB flash drive while the 250 does't. For example: if you put the same hard drive in both consoles, say the 250GB hard drive, then the 4GB version would have 259GB as the 4GB is onboard and will allow the 250GB hard drive. The 250GB version has no onboard flash drive so it remains at 250GB