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You may get a wide variety of opinions on this one. Personally, I greatly prefer the Conn Helleberg. I believe it to be a better proportioned mouthpiece. I say this with the knowledge that both are quite popular mouthpieces, especially in public schools. The 24AW has a somewhat smaller diameter, with a fairly large depth to it. The Helleberg is a bit wider in diameter, with a good bit of depth. I use the Hellberg with my Miraphone 186 for a good deal of playing. Although I own a 24AW, I have not used it for many, many moons.

As far as the sound produced, I find the Helleberg produces a very full and rich sound.

A 24AW is shallower, and narrower than the standard Helleberg, but has a wider, more rounded rim. It is also more of a bowl shaped cup vs. the funnel shape of a Helleberg. The standard Conn Helleberg has a very sharp inner rim which can provide clean articulation, but some may find uncomfortable.

When I started playing again, after an 18 yr hiatus, I began using the (Benge) 24AW that came with the tuba I bought. I found it to be a little narrow for my taste. I bought a Conn Helleberg as a replacement and I also found that I was more comfortable with more of a funnel shaped cup vs. the bowl shaped, at least on the King 2341 (2 piece) that I started playing on. This will be a matter of personal preference, so nobody can really tell you what will work best for you.

Either mouthpiece would be an decent choice to get back into playing with, and I would consider them both to be good "general purpose" pieces.