As you go from hozozao to chuuzao to futosao shamisen, the dou gets bigger in size. The differences in dimensions are small (especially between hozo and chuu sao) however there is a big impact on depth and volume of sound. Supposedly this came about as the shamisen moved from performances inside in close environments (e.g. kouuta) to outside, open environments (gidayu, tsugaru).
Can you play the various styles on other types of shamisen? My two cents: Yes, but you may change the mood. This is true for music in general. Playing a soft and intimate kouuta piece on a tsugaru instrument will not have the same effect. Also, different styles use somewhat different fingering positions so some notes may be played flatter than on other styles.
There is a lot of misinformation on shamisen. It is NOT true that all shamisen have the same neck length (and I am speaking of only standard size shamisen). In fact, a chuuzao “minyou” shamisen sao is shorter than a chuuzao jiuta one. There are also short versions of some shamisen and these are standard instruments.
As for me, I have minyou, jiuta and tsugaru style shamisen. I like the traditional music and prefer jiuta, although it is fun to make a lot of noise with tsugaru once in a while.