The short version
Headspace is curriculum-led teaching under one voice; Insight Timer is what Insight Timer calls the largest free meditation library. Pick on whether you want structured learning or open exploration.
When is Headspace the right pick?
If you want a structured introduction to mindfulness with a clear curriculum and a consistent teaching voice, Headspace is the right shape. The Basics course is one of the most structured beginner paths in the category; the $70/year subscription is the cost of curated polish.
When is Insight Timer the right pick?
If you want what Insight Timer calls the largest free meditation library — access to Tara Brach, Jack Kornfield and thousands of other teachers at no cost — Insight Timer is the right shape. The free tier is genuinely free; Member Plus is optional.