Well you would have to have the other phone and it would have to function. So if you either don't have it, or it is damaged and not working, then there is no way you are going to get anything off it. If you have it and it is damages, you would have to repair it first to access the data.
Now if it is working, and you still have it, then you can simply connect the phone to a computer via USB cord and move all the files (not apps) over to an empty folder on the computer. Then disconnect that device and connect your new phone to the computer. Now you just do it in reverse and move the files over to the phone or its SD card from the computer.