Flugelhorn tops come in a regular (FLC), deep (D), and shallow (FLS), cup.
The FLC flugelhorn top provides an excellent combination of a dark tone and access to the upper register. This is the best choice for most players.
The British Cornet / Flugelhorn D top is a dual purpose top the works equally well as a deep flugelhorn top or as an extra deep cornet top. The cup is a deeper option that provides an extra dark sound, but the trade-off is an upper register that is less supported. It can be used on either instrument with the appropriate shank.