My impression is that radio taiso is quite a bit tamer than dancing grannies. The former is usually mellow with slower tempos and relaxing uplifting vibes and it's really meant to be something for all ages; the latter is closer to electronic/club music, with faster tempos, and more aggressive beats (and yes, it's quite a bit louder too).
In my experience, radio taiso also inherits a lot of the japanese polite culture. When I was young, my experience was that radio taiso always took consideration of surroundings: it was always in a designated space and time (e.g. the school gymnasium before class), whereas my experience w/ dancing grannies is that they just kinda make a habit of showing up at privately owned public spaces (e.g. malls) early enough in the morning and in a large enough group of people that security guards don't want to bother dealing with them.