I don’t think there is much difference between the use of the words tuxedo or bullseye to describe a watch dial.
It is likely that over the years the dials to which the term has been applied has widened from the original intent.
Personally I usually associate tuxedo dials with UG or Rolex and bullseye with Omega.
The FLE could be described as either, with challenge only likely from pedants.
Perhaps this for an approach…
You are feeling in a 70s vintage mode - go with bullseye.
You haven’t memorised the reference number of the most recent Rolex models to use a tuxedo dial, but want to demonstrate your credentials to the Rolex devotees at the local GTG - go with Tuxedo (CW are after all the Rolex of the internet).