Why should you use a stateful hardware wallet?
A hardware (HW) wallet drastically reduces the attack surface. By contrast, a computer can be hacked much more easily, allowing an attacker to steal your key material. Whenever you sign anything with a HW wallet, always verify the destination address, amount, and fee on the wallet’s own display, because a compromised computer may show you something different from what you are actually signing.
A stateful HW wallet lets you keep the key material (the seed phrase) in a more secure location than your computer. Ideally, it should contain a secure element that makes extracting the key material significantly harder, though you should still assume it could eventually be broken.
If you use a stateless device such as the SeedSigner or Jade (in stateless mode), you must carry the key material with you. This makes it far easier to steal or, even worse, to copy without your knowledge.