Does it matter? Yes. Everything matters. Everything makes a difference.
The
real question is does it make a
noticeable difference. And of course, the answer to that question is,
"It depends."
I'm not trying to be a smart-***, even though I do live in Missouri; I'm just saying it like it is. Sometimes it does, other times it doesn't, depending on the player, horn, mouthpiece, repertoire, etc., in combination. I feel better with my Curry 128D on my upright bell, and my Kanstul custom on my recording bell of the very same tuba. My Kelly 18 does reasonably well on both, especially for outdoor concerts.
No mouthpiece is the magic answer. Find one that feels good, blows well with the tuba, helps you get a reasonable tonality and intonation, and stick with it.
I, too, confess to my own mouthpiece safari over the past years, as do other tuba players. But I borrowed a lot first and made notes as to what felt good and what didn't, and was able to narrow my scope considerably as a result. Then I asked for recommendations from folks who know such things for my primary mouthpiece, taking a frank inventory of my strengths as a tuba player, but more importantly, my weaknesses. Once the primary was resolved, I indulged in a few secondaries which serve me well. So, my current shelf lineup is:
#1) Curry 128D with the rim narrowed to Bach 18 contour for the upright bell;
#2) Kanstul custom 18 (my preferred cup i.d.);
#3) Kelly 18 for outdoor use;
#4) Bach 18 as a spare (and with its slightly larger throat works well for me for sustained higher register playing and the rare solo);
#5) G&W Taku Lite that is a reserve in case I am in a position to borrow a tuba, and I can go through all five to see what will work for the day. It's a little stuffy on my 186, but I'm hoping it will do well on an Eb tuba.
#6) Another Kelly 18 that, surprisingly, works on stuffy tubas but not on free blowing tubas, in contrast to #3 that seems to work better on my 186 and freer blowing tubas, but not on stuffy tubas. Go figure.
I'm considering an Eb tuba. Will I go on safari again? Probably. I've owned or had access to other tubas and sousaphones in the past. The mouthpieces that worked best for me on them did not work as well as the above on my 186, so when the horn went, so did the mouthpiece.
The key to a tuba mouthpiece safari is to first get a good horn, then try or borrow as many different mouthpieces as you can to see what feels the best, note their attributes, and then narrow the universe for models that have similar characteristics. For example, I like a Bach 18 style rim, 1.28 cup i.d., @.325 throat. The depth of cup and backbore are the variables I have to try with any particular horn to see if I like the way it feels, blows, and intonates.
After that, try to purchase used so if it doesn't work out you can flip it to the next person on safari for no, or very little, loss on the deal. I am lucky. My #1 and #2 I purchased new to order, and they have been what I needed. But only after I followed the above approach for a couple of years.
Here is a great comprehensive chart for mouthpieces sorted by cup i.d. Use it like a naturalist uses a field guide to get him into a good position to observe the species under study. Do not use it like an engineer's manual to fit mouthpiece A to tuba B.
http://www.allbrassradio.com/tubampccharts.htm" target="_blank" target="_blank" target="_blank" target="_blank
Doug Elliot has a great chart that also compares the cup depths as well.
David Werden also has a great chart that compares rims, throats, backbores and other criteria as well.
But no chart can precisely chart the cup geometry or how it will interact as the interface between, player, instrument and the music. So some trial is necessary.
Again, to the top: does it matter? Yes, or at least we all think it does, otherwise folks wouldn't be churning out new mouthpieces and mouthpiece designs? Does it make a
noticable difference out front in playing? It depends on all the above, and more.
(Yes, Kelly now advertises a wider cup. But when I got mine, it was/is the 1.28.)