I grew up in England and my first tuba was a BBb (ancient Hawkes high pitch conversion) - that is all my school had to lend me. When I had saved up enough money to buy my own tuba (decent 2nd hand ones at a reasonable price were hard to find in England in 1972) I ended up getting a B&H Imperial Eb - I still have it. I found that the transition was comparatively easy since the fingering was identical in a portion of the range (and if I got confused I could always just hold down the 4th valve
35 years later, when it came to get a new instrument, the choice was really between a CC, BBb or Eb - times had changed and I had moved across the pond where CCs were common. I considered moving to a CC but realised that (re)learning the fingering would be much easier if I moved back to a BBb. I might also have stuck with getting a new Eb but liked the idea of having 2 complementary instruments to use rather than getting simply a replacement. I have no aspirations towards getting a professional job so that is not a factor in my decision.
Translating this experience to the likely scenario prompting the OP would suggest that if the student already knows BBb - get an Eb. If they already know CC - get an F. Of course, as I said there are many different factors involved and everyone's situation is different - this is just one amateur's experience to feed into the mix.






