Mix of the both. Simplified: damage = base atk (stats) * assault (from weapon skill/char atk eidos) * ele damage (from ele eidos, ele advantage, etc.)
So 40k attack (as shown for the KH in the edit window) with 0% assault will do the same damage as 20k attack with 100% assault. Both are important, but leveling your assault weapons is usually the fastest way to get stronger, since increasing the base stats usually takes some time (max broken event SSRs, accessories, +99s, etc).