The 3870 is more powerful than the 3850 just because it is... Not sure exactly why. Probably the architecture/higher clock speeds. Why is the 8800GTX faster than the 8600? I dont think you would be able to clock a 3850 to be faster than a 3870 without doing a volt mod, and you wont be able to go that high with the small cooler on the 3850.
Not much. Overclocking may only add about 5fps onto games with 100MHz added. Probably with a stock cooler, I would say about an extra 50Mhz on the Core and maybe 80-100Mhz on the vram max.
Typically the stock cooler doesn't affect how far you can overclock unless you're voltmodding, which I do not recommend. How far you can overclock a 3800 is more down to luck of the draw, but since a 3850 is pretty much an underclocked 3870, you should fare well with it.