V1 for the GO case is computed for an engine failure condition.
V1 for the STOP case is thought for any kind of failure (other than braking systems...)
So if I ever have a malfunction different than an engine failure at or above V1I know that I can continue take off very well!. The airplane will lift off and climb as in a normal take off. In the STOP case, however, there is always a reasonable chance to overrun or depart the runway no matter what kind of failure you have, engine or anything else.
As a rule, GO is better than STOP, the only exceptions being failures or circumstances of a catastrophic nature that render the airplane "unflyable" (terrorist bomb explosion, total flight controls failure...).
The question is "How the heck I know the airplane is unflyable?"