The viola does drag a little compared to the violin, even with the best bow technique. It takes slightly longer for the string to start sounding. But with good technique it should still be able to handle any fiddle tune -- some classical viola parts contain passages that are faster than the fastest fiddle music and you can still hear every note crisply if played with good technique.
The viola needs extra attention to coordination between the hands. You need to start moving a bit earlier to play on the beat. Eventually it becomes second nature.
But it should be more pronounced on the cello, right ? this "time delay" for sound production. (But as you're more used to the cello, maybe the cello bowing is second nature to you which makes it less noticeable ?)
I too find the violin "more responsive", after flddling with the violin I find it difficult to switch to the viola (which I still prefer, though).
Or perhaps the different posture and bowing technique are more conducive to a quick response? I'm not familiar enough with cello technique to be sure, but the way we hold a violin or viola limits the amount of weight we can put on the bow and perhaps dexterity when putting a lot of weight on the bow.
A couple more thoughts on viola response and its limits:
Playing fast notes on viola gets tiring much faster than on violin, even if you're not approaching the instrument's physical limitations -- it's simply more work to get the string moving on every note.
Technique isn't the only important thing; I also think it's more important to stay on top of equipment maintenance with viola than with violin. Old strings and and old bow hair can make the viola much slower, especially on the C and G strings. When working on Borodin's 2nd Symphony for a concert the fall before the pandemic, I found the fourth movement unplayable on 6-month-old strings and 9-month-old bow hair because my C and G strings just felt sluggish. After breaking in a new set of strings and getting my bow rehaired, it became much easier.
It may be a little different to coax a fiddling tune out of a viola, but isn't it worth it to end up with something like this?
Nothing wrong with a slow jig!