Can you Defy Quickdraw equipment like Long Sword?

No — Defy can't counter a Quick-Draw Equipment like Long Sword, and cost isn't the reason (Long Sword's printed 2 energy + 1 power is well within Defy's limit).

Defy counters a spell, and a Gear card never sits on the chain as one. Playing Long Sword puts it on the chain as Pending, then it finalizes and, being a permanent, resolves immediately onto the board (Rules 337.2, 359.2) — finalizing doesn't pass priority (337.1.a), so there's no window where you can point Defy at it. By the time you have priority, the Sword is already at their Base and attached via Quick-Draw. Quick-Draw's "attach it" effect does go on the chain separately, but that's a triggered ability, not a spell, so it's not a Defy target either (Rule 133.4.b, 351.1).

To beat Equipment, you need effects that Kill, banish, or detach the Gear itself — Defy only answers true Spell cards.