If someone plays Counter Strike Jax sig spell and I have more might as the attacker, do I move back to base as the attacker or would the defender move back to base?

You move back to base (via Recall) — the defending unit stays.

Counter Strike prevents all damage to the chosen unit in the Combat Damage Step, so even though your unit has more Might and dealt lethal damage, it was prevented and the defender survives. Since both you and the defender still have units at the battlefield after damage, the result is "No Result" and the attacking units are recalled to base (Rule 461.1.a.2). Relative Might doesn't decide who leaves — only whether defenders remain does. Note that this return is a Recall, not a Move, so anything that triggers on "when I move" won't fire.