The answer is a big it depends.
Most design and coding work can probably easily be done on a five-years-old computer, in particular if you do not need fancily looking operating systems or similar stuff with no direct relation to the work.
However, in both professions you can reach the point where computational power begins to limit your capabilities. For example, if a programmer regularly needs to recompile large chunks of code or runs intensive tests or data analyses or if a graphic designer needs to intensively apply complicated filters, works with 3D software or does a lot of batch processing.
So, even if one profession needs more computational power than the other on average, the ranges of the actual needs are very big and overlapping. Therefore this would not allow you do make any general claims such as you are looking for as you need to look at the individual situation.