The rotary Bb-Trumpet with 4 valves is a complete Bb-Trumpet. The 4th valve makes it easier to reach the low tone ranges. This results in an expansion in the tonal range at the lower end. In addition, all 4th valves are designed in a way that the quart valve can be converted to a quint valve by a crook.
But this is only one of the many advantages. The extra valve gives the instrument additional mass rendering the sound more voluminous and pithy.
The 4th valve also allows for alternative chords. This facilitates playing notes which are difficult to intonate, but what is even more interesting: notes played with the 4th valve have a different tone quality. For example, a d played with the 4th valve sounds much more free than when played with the 1st and 3rd valve. This allows for more flexibility and a richer sound quality.
A deep trumpet is required in the romantic and modern orchestra literature. In the romanticism the low (mostly in F- tuning) trumpet was the standard instrument. The upcoming B flat trumpet was called high trumpet under which today mostly Piccolo trumpets are understood).
So it happens that Richard Strauss, for example, demands tones in his pieces that cannot be played on the instruments in use today. This also happens with other composers. The THEIN 4-valve Bb trumpet is ideal for this. The fifth bow, for example, makes it easy to play even very high bass trumpet passages, as required by Henze, for example.