The baroque trombone is basically the same as the rennaisance models, just with some minor changes of comfort. It appeared around 1700.
The Bell is almost un-flared, and thus produces a very humble , almost "dull" sound. It was used foremost in the church-music, to accompany the vocalists, but also in the "streets" atogether with shawns.

Rudolph Meinl - Alto, Tenor & Bass trombones

The mouthpieces used to these instruments are quite special, and need some extensive practising. As modern mouthpieces are all-around quite soft - these barock-mouthpieces are all edgy and are quite unconfortable to play on. Sometimes the hard edges can be so unfitting for certain players, that a very nasty "air-sound" will be produced. These players should look for other mouthpieces, or try to develop their own models, as I can't believe that this was supposed to be - even in the old times.

Egger mouthpiece

The music played on barocktrombones is basically from early music - until the classic era starts. Mozart certainly didn't hear these trombones in Wien, where he lived. So to play a tuba mirum on a baroque trombone is probably not really the proper case.

R.Meinl Alto trombone