If I play Divine Judgment, can I wait for my opponent to react or not before I decide on recycling my runes for power? Does the answer change if they decide to do the same?

No — you must recycle the runes for the 2 Power when you play Divine Judgment, before your opponent gets any chance to respond.

The Power cost is part of the printed cost of the card, paid during Step 4 of the play process (Rule 357). The card isn't finalized on the Chain until costs are paid, and your opponent's Reaction window only opens after finalization (Rule 338.2). You can't float the payment to resolution — that's not a choice Divine Judgment gives you.

If your opponent responds by recycling their own runes, the answer doesn't change for you. Your cost was already locked in when you played the card. Their recycling is their own separate decision (they can float Power in reaction to survive your spell), but it doesn't reopen your window — and once they take a game action, you can no longer reverse your rune-recycling decision anyway (Tournament Rule 509).

This is the exact opposite of Bullet Time, whose "pay any amount of power" happens during the card's resolution — there you can wait to see reactions before committing (FAQ #8161).