I am lucky to be in a band and be on call with a few folks for all three: tuba, DB & EB. I've played EB since 1976 when I was 14 years old in summer jazz band camp and learned how to read charts on the fly (handed my first charts on a Monday morning, played a concert that Friday evening). But here's where it's really interesting: the jazz band I play with now had EB players for years and years. Good players. They sounded fine, and the band sounded fine. They hire me. I play the charts well. But the more I play with them, the more I start to feel something is "missing." I realised that with the push and sustain of the EB, some of the swing charts sounded "pushed" or "edgy." So I changed from my "straight ahead" EB style with roundwounds. After a few months of experimenting with EB flat strings, shoving foam rubber under the bridge cover, different techniques, no compression, etc., it still just wasn't happening. So I went out and purchased a CCB with the $$ I could afford, spent several months getting it set up, finding a good set of used Spiros, Full Circle, new amp, practicing my @$$ off, and finally took it to a rehearsal after talking to the band leader about it. The character of the band immediately changed, and the swing charts started to really swing again.
This same band had an Independence Day gig a couple of years ago, and the tuba was indispensible for the Sousa marches and such. It just would not have happened well on either DB or EB. What I have mostly learned from 35+ years of playing everything from garage bands to national TV, from Friday night to Sunday morning, bars, shows, pits, church, even Dixieland funerals, is that each instrument has its place and its gigs. For the average guy like me who still earns income primarily from a day job, I really encourage a player to learn to play all three to be most available for the most number of possible gigs.