shadows of the past do both users recycle units to hands

Yes — you can pull units from both players' trashes.

Shadows of the Past reads "Return up to 2 units from trashes to their owners' hands." "Trashes" is plural, so you may pick from your own trash, your opponent's trash, or any mix — up to 2 units total. Each unit goes to its owner's hand (Rule 56), so if you grab a unit out of your opponent's trash, it goes to their hand, not yours.

One correction on wording: this is return to hand, not Recycle — Recycle is a separate game action that puts cards on the bottom of the deck (Rule 416). Also, "up to 2" means you can choose 0, 1, or 2 units; you're never forced to pick any.