Comments based on past ownership of a Holton MF st307, Wild Thing, Inderbinen Alpha C trumpet and a good blow through a Schilke s22 (which only confirmed what I felt about the other instruments).
The first time I switched from a standard bore instrument, and attempted to play it as I would the standard bore, it was an awful lot louder and pulled significantly more air. Just as the mythology says. But after a while, I wised up and eased off on the oral pressure to better match the volume of the standard (then as now, the Yamaha 6335H II). The physics tells me they should still draw a little more air for a given note, but not so much as I could notice the difference. The difference I did notice is that they became distinctly more mellow in sound (which those of you familiar with my postings will know is not a good thing in my books - I don't play cornet).
I rather unenthusiastically tried to brighten the sound with a smaller piece, but, as with J. Jericho's experience, ran into problems with mismatching between cup size, throat and bore resulting in a more 'strangled', less resonant sound. Not good.
Best compromise piece I have found is the Wick 4C, which has the added bonus of being a little less punishing on the lip than the birdbaths I used to play. But you do lose something of the full force of these instruments played through a proportionally large throat. Hypothetical anyway - I just can't do that anymore.
What I ended up doing is splitting my repertoire. The stuff which called for a brighter sound like baroque classics etc, I played on the ML Yamaha or Severinsen - the more mellow (or just louder) stuff - I played on the Wild Thing.
I do find the Wild Thing remarkably easy to play. Ideal student trumpet in my view. And that is not a criticism - just an observation based on playing it for nearly 20 years. When I'm working on tonguing and flexibility, I reach immediately for the Wild Thing because that's the instrument I'll crack the problem with. But I don't think this has much if anything to do with bore size - more the resonant design. The stronger slotting instruments like the Yamaha are for me much less helpful in problem solving. They're maybe more for those whose technical issues are behind them. But I digress.