For completeness I added the Trezor key (dropbox lets you have multiple security keys attached to your account), then removed the Ledger Key... logged out and tried to log back in with the Ledger Key... and got the same message. So, DropBox sees them as 2 unique keys.
Based on this quick and hardly thorough test, it would seem to suggest that the U2F is not cross-compatible between different brands of device, even with the same seed.
Probably the U2F protocol implies that the technical characteristics of the U2F key (its brand and manufacturer) must be the same in order to satisfy the protocol. And this is entirely logical, because it is thanks to this that increased security is achieved when using these keys. Based on this quick and hardly thorough test, it would seem to suggest that the U2F is not cross-compatible between different brands of device, even with the same seed.
It would probably be surprising if you could recover your key using a seed phrase using any device of this kind produced by different manufacturers. The fact that the dropbox sees these keys as if they are different is our additional guarantee in case someone becomes the owner of our seed phrase and wants to restore the key on another device without knowing about this feature.
I wonder if there are any exceptions to this rule? Maybe among the whole variety of keys from different manufacturers, there are still some that would be interchangeable with respect to each other.
It would be interesting if someone did such a large-scale study.