If I play Flurry of Feathers, do I have to choose which effect I'm doing on finalization or resolution?

Finalization — you pick the mode as you play it, and it's locked in from there.

Rule 355.3 is directly on point: for spells and abilities with a bulleted list of modes, you make that choice during the "make relevant choices" step of finalizing, alongside targets. Resolution is just executing the mode you already picked (Rule 340.1) — there's no swapping it later.

Two practical consequences: if you choose Counter a spell, you must have a legal spell on the chain to target when you finalize Flurry, or that mode isn't a legal choice; and if you choose the tokens instead, the battlefield-or-base destination for those four Birds is also locked in at finalization, so reacting with Gust or killing your unit beforehand doesn't relocate them.