Since
Arnor fell apart into three "petty
kingdoms" in 861 Third Age upon the death of King Eärendur, Arnor's "peak" cannot have amounted to much.
Fonstad (from your son's other question" estimates
Gondor to be twice as large as Arnor - the "core kingdom", not Gondor at the height of its power, which she estimates to be about three times as large. If we then assume that Gondor had something closer to a Mediterranean climate, while Arnor would have been closer to England and its neighbors across the North Sea and English Channel (but in both vases more of a continental climate), then we can assume Gondor's population density to have been greater. With Gondor reaching its peak of power almost 300 years after the division of Arnor, I'd thinks it's absolutely no contest that Gondor at its peak was far stronger than Arnor at its peak, whenever that may have been.