Take a gander at this, Razblade.
It’s a comparison of tone between nice hosozao, chuuzao, and futozao shamisen.
From 3:14 the player repeats the same song (Ringo Bushi, a folk piece from the birthplace of Tsugaru, Aomori Prefecture) on each type.
As others have said, you’ll hear a much stronger percussive play style with the chuuzao, and even more so on the futozao/tsugaru.
A nagauta has a bit of it, but the traditionally higher action of the bridge and smaller resonator tend to undermine it.
I don’t want to dissuade you from saving up for a tsugaru (the cheapest of which I’ve seen retail around $750.) But this video really demonstrates the difference a professional player can pull out.
You can play anything on anything. The shamisen is fundamentally a folk instrument; you play what you know with what you got.
If we want to split hairs about what comes out as the most flexible, I’d suggest a chuuzao shamisen with an adjustable sawari.
A middle sized neck is big enough for comfortably executing tsugaru techniques and fingering, but won’t be overwhelming heavy and wide like a futozao can be.
An en or azuma sawari gives you more tuning flexibility.
With a typical min’yo body, you’d get a higher pitched, guitar-like sound (closer to the nagauta spectrum) and with a typical jiuta body, you’ll get a slightly deeper, more bass-like sound. (Closer to the tsugaru spectrum).
By messing around with string guages, koma heights, and playing styles, you can get all sorts of neat sounds out of it.