Side panels may interchange. Not sure if hood panels will - we moved a loader from a D14 to a D15 Series II and had to add 1" to the loader frame cross bar going over the gas tank, so the D15 is a hair wider somewhere (either front frame, rear axle points, or both).
Both had a 149 cubic inch engine (gasoline), so perhaps the carb and starter would interchange. The only way to know for sure is to look at a parts manual for each tractor and see if the part numbers are the same. Tyr posting the part numbers from your parts manual for the D14 and see if someone with a D15 parts manual can help you out (I'm going to buy one but just haven't gotten there yet ...)