Garen vs Jax Top Matchup
Garen Top wins 55.9% of 5,938 Low Elo games against Jax Top, +3.5 points vs expected, 2-patch window 26.19-26.20.
Researched on LoL patch 26.20. Tips are written to hold at any rank; stats come from Low Elo ranked games up to patch 26.20.
Why Garen is favored
Jax's Counter Strike(E) can avoid Garen's attack-based Decisive Strike(Q), but it does not stop Judgment(E) from dealing damage. Garen can spin through the dodge window, use Courage(W) around Jax's stun, and silence him after Counter Strike ends, which makes Jax's timing key to winning an extended trade.
How to play as Garen
Do not use Decisive Strike(Q) into Counter Strike(E). Spin with Judgment(E) while Jax dodges attacks, then time Courage(W) for the stun and use Q after his dodge ends.
Counter Strike(E) dodges attacks, but Judgment(E) is a spinning area attack and can keep damaging Jax during that window.
Courage(W) gives Garen a brief shield and tenacity, which can help him absorb damage and shorten the stun window at the end of Counter Strike(E).
How to play as Jax
Use Counter Strike(E) to avoid Garen's Decisive Strike(Q), but do not expect it to stop Judgment(E); leave the spin's range and re-engage after it ends.
Sources
These notes come from r/GarenMains, checked against the champions' abilities.