Strategy at ai lab vs product at startup

Three offers: 1. Strategy at top ai lab (think OpenAI/anthropic/google brain) vs 2. Product at hot a16z backed startup (~100 employees) vs 3. Product at established unicorn (square/brex type company) I’m very interested in ai - but would probably rather do product work than strategy work. 1. How should I think abt switching into product from strategy - especially at a tier 1 brand name 2. How unique is the opportunity to join a top ai lab? Does that outweigh not starting in my ideal function?