In theory; in practice, one reliably and repeatably works, and the other I'm not sure (and not willing to find out.) I've had some experience with stolen checks; while the money has been ultimately returned to me, it was a major hassle, and cost me several sleepless nights.
> How does Apple Pay factor in here?
Apple Pay gives the merchant a generated CC number (per-card, per-device) with a generated one-time security code (for every single purchase.) If the merchant is breached, all the hackers are getting is a generated CC number and a (expired after single use) security code, so they can't charge my Apple Pay card at all — and of course not my real card (which has never been exposed to the merchant to begin with.) The easiest and fastest chargeback is when there is no charge!