If a hardware signing device does not store your seed, the hardware itself is only a computation device whereas a hardware signing device that stores your key is both a vault and a computation device.

Not implementing the vault functionality means that at least you cannot mess that part up as an implementor, so that's good. However, it also means the device defers all vaulting security to the user.

Depending on your use-case this can be good or bad:

If you use this for true cold storage that you only need to touch in major life events: (i.e. to pay the hospital that saved your life, to buy a house) then physically separating key-parts (seed-parts) makes sense. After all, you don't need your private key to put funds INTO your cold storage thanks to BIP32 extended public keys: you can put each utxo on a separate key yet never touch your seed. You will however have to properly secure your seed(parts) by yourself; don't mess that up.

If on the other hand you use your signing device daily, then this isn't cold storage but a lukewarm wallet / cache. Storing a key for that inside your signing device makes sense, because you do not want to handle (=expose) your seed all the time. Look at this use-case as having an air-gapped device that you keep close and use occasionally, this is for example where you fund from / submarine swap to with your LN wallet. It makes sense for this to not be your cold storage stash.

My ColdCard stores my seed but my SeedSigner does NOT store my seed.

I feel like generally the biggest upside to having a hww is being able to sign for things without the admin of punching your seed in every time, and ideally keeping your seed offline - never touching a internet connected device etc