Celery will take up water much quicker and eveen small changes in mass can be measured more accurately. The Celery has xylem vessels running through it whereas the potato does not therefore the celery can transport water much more quickly. With potatoes however, thick skin and vast amounts of carbohydrates slow the uptake of water. It can also be difficult to tell changes in mass.
If you are cutting or boring the 2, celery is much easier to get equal size pieces of due to being 'crisp' and generally uniform. Sucrose solution will also have a greater effect on celery and as before, this will make it easier to distinguish changes.
Economically, celery is cheaper than potatoes but for c/w this does not matter.