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I've been doing some research and it appears this can be done with either, but traditionally, which horn is best suited for this piece of music in an orchestra?

I think the standard non-answer would be that it depends on what works for you and your group.

Glancing at the part on IMSLP, however, I personally would lean heavily toward contrabass.

This one lies well for either horn if I remember. I played it on CC because that's the one I used on every other piece. I wouldn't drag a second horn to rehearsal/stage if I was not using the "other" horn. If you use Contrabass on the rest of the pieces, use contrabass and vice versa for Bass. Just my thinking on it, but I would lean towards contrabass if I could.

Funny part is everything I'm playing is bass tuba stuff (Poulenc double piano concerto, Berlioz Fantastique)

Play that fine Rudy Meinl for everything. That tuba stays home for nobody!

But really, the Eb should be okay for Hall of the Mountain King, if you are alongside a strong bass trombone player and the brightness of the Eb blends well with it.

I have some strong confidence in the bass bone player.

Bill Bell told me that he used his Eb sousaphone for most of his solo LP, but he used a BBb tuba for Mountain King. You can really hear the difference.

However best you can cleanly articulate and present those two important F#s below the staff toward the end of the piece

bort wrote:Play that fine Rudy Meinl for everything. That tuba stays home for nobody!

I totally imagined this as the line, "Nobody puts Baby in a corner." from Dirty Dancing.