Yes,
Arbor Elf can untap a Stomping Grounds to get you red mana, that's good. It can also untap a land enchanted by
Verdant Haven to give you TWO mana, that's also good. It can even untap a land enchanted by
Underworld connections to draw you an extra card! In almost all situations,
Arbor Elf will have an advantage, especially in casual play.
Llanowar elves have an advantage though, their ability is a Mana Ability* so it can't be responded to. If your opponent had a
demolish, if you activated
Arbor Elf targeting your Stomping Grounds, they could
demolish it in response and deny you the mana. If you activate a Llanowar Elf, there's no
opportunity for response, so you're going to get the mana even if they have a
doom blade. In even more niche cases,
Arbor Elf gives your opponent the
opportunity to cast a spell before your first spell during that phase, which can (rarely) be disadvantageous. So rarely that I can't think up an example right now! But if you're getting into high-level competetive play you should be considering this.
TL;DR: In Casual play,
Arbor Elf is strictly better, for the exact reason that you mentioned, as well synergy with cards like
Utopia Sprawl.
605.1a. An activated ability is a mana ability if it meets three criteria: it doesn't have a target, it could put mana into a player's mana pool when it resolves, and it's not a loyalty ability.