As a former brass instrument player I have tried many different types of mouthpieces and have had a lot of different experiences from using them.
I use what is considered a beginners mouthpiece, but I feel I am most comfortable with it. The only difference than a regular mouthpiece is that it is flatter where you put your lips on the mouthpiece and I feel more comfortable using it than a regular mouthpiece. I cannot explain it but it seems to me it is just easier to play the instrument and make the sound I wanted.
I have also played using plastic mouthpieces and even a gold mouthpiece. I absolutely hated the plastic mouthpieces with a passion as they made a really hollow sound when I played and I felt I had to blow a lot harder to make the sound I wanted. The gold mouthpiece I felt had little difference except for aesthetic reasons.