Good question John. I only use cutaway tenor ukes, Florentine, Venetian and tapered, and don't find any loss of volume. I've also read somewhere on the net that there's no perceptible loss of volume with cutaway.
This is Michael Kohan in Los Angeles, Beverly Grove near the Beverly Center
9 tenor cutaway ukes, 4 acoustic bass ukes, 12 solid body bass ukes, 14 mini electric bass guitars (Total: 39)
If you're talking about sound volume, my guess is you'd be hard-pressed to be able to hear the difference. But it seems like the scalloped/beveled would be the smallest change. And florentine and venetian would be more or less the same, just differing aesthetically.
There seems to be an assumption that reducing the capacity of the body - or is it the area of the top? - will inevitably lead to a reduction in the volume of sound produced. I doubt it, and would suggest that other factors are much more likely to have an effect.
At one time I owned a tenor 2009 Pono PTEC-CE Cedar/Ebony cutaway paddlehead and a 2013 Pono ETSH-PCC Cedar/Ebony slothead double bout at the same time. (Don't ask.) Both were strung with Living Waters Low-G sets. The sound was different between the two of them. The double bout sounded slightly "fuller" than the cutaway. A bit boomier towards the base end. But the loudness was pretty equal.
Both were made in Java and assembled in Oahu. Of course they were made in two different years. Who knows if the bracing, wood thickness, glues, quality of wood, construction methods etc. changed in those 4 years?
Oh, and the cutaway has a Pono passive piezo pickup installed. Original I believe.
Does this settle anything? Nope. It could have been all in my head. An unconscious bias. And I didn't have a meter to measure the loudness.
FWIW: I prefer the Venetian style cutaway to the Florentine. But I think the Scoop is the classiest looking of all. Alas, I don't own a tenor with one—yet?
One common question is whether a cutaway diminishes the tonal output of an acoustic guitar in a significant way. The truth is not by much, because that particular portion of the soundboard doesn't drive a lot of the tonal output. The taper of a guitar's waist will actually have more of an impact on tone. Our opinion is that the access you gain to the upper register notes from a cutaway far exceeds the minimal reduction in tonal output.
I probably should mention that Taylor company is know for good marketing and their guitars are known for having cutaways... so the info may be slightly biased. But, I don't think they'd give you very misleading info.