Both on bottom, or one on top?

[DonShirer]

I agree that this is probably a non-issue. I take the upper part on my Eb, but if you only have Bb's and neither one of you feels comfortable with the upper part, by all means take the lower part unless the conductor complains.

[jimgray]

Allow me to offer my somewhat unusual perspective-

I believe that a strong tuba player is generally in a better position to make register decisions in band music than many band conductors, arrangers or composers for that matter.

Please note that I focus this on band music specifically - don't try this in your orchestra!
Much of the band repertoire consists of transcriptions, and all of it very subject to flexible numbers of instruments per part, etc.
There are many, many factors that influence whether Jim should decide to play an unwritten low Eb or not.
And those factors may change within the context of a performance, so asking the conductor isn't even always an option (if I wanted to, which I usually don't).

I'd much rather exercise my own best musical judgment with regard to register, in the same way that I make choices about relative dynamic, articulation, and thousands of other things. It's more fun that way, but it's also more spontaneously musical.

Of course, this only works if you have the trust of your conductor and standmate(s).
Earn that first, then play whatever you want, as long as it moves the music forward-

For the record, there are some serious composers of band music that I wouldn't exercise my judgement on quite so freely as others.
Hindemith, Dahl, etc. If things are deliberately and specifically engineered to perfection, don't screw with them.
Otherwise...

cheers-
Jim Gray