In my experience, this is wholly based on what element the mob is. In FFXI, certain spells were stronger because it wouldn't have felt right to get the same damage out of Stone that you get in single digit levels vs. Thunder that you get much later on. You wanted to feel like you were progressing, so spells that you earned at higher levels hit harder.
In FFXIV, you learn all your elemental spells at the exact same time; there's no need for one to feel stronger than the others. You want to target it to the elemental weakness (or, non-strength) of the monster you're fighting, not just assume that one spell is going to be the most potent.
Also, elemental points that you gain from leveling increase the effectiveness of the corresponding spell. I haven't noticed this being especially potent yet, but "it is what it is."