In order to determine the difference in size you must calculate the contribution of conduction through the tube wall to the overall heat transfer coefficient.  If the film coefficients for the tube and shell side fluids are quite high then it is likely that changing the tubes from copper to stainless will require more area. It is also likely that the tubeside film coefficient will change due to a change in i.d.  Utilize the calculation of overall heat transfer coefficient to determine the new size of the exchanger.  See Perry's Chemical Engineers’ Handbook – Chapter 11.