What's the best way to track brand perception shifts after a product launch?

Do both, but sequence them — start with social listening (Brandwatch or even just Sprout Social) to get a quick pulse on organic sentiment, then run a short brand tracker survey (10-15 questions max) about 4-6 weeks post-launch to measure awareness and perception shifts against your pre-launch baseline. The key is having that baseline; if you didn't run one before launch, set it up now so you at least have a benchmark for 3 and 6 months out.