I liken the Ki-61 to a bobsled. It'll go pretty fast in a downhill run, but once you get on the deck and turnfighting, you're going to get outrun in a level dash by any of the late-war planes. On the other hand, because you're slower, you can turn tighter without blacking out due to G's. Also, having two nose-mounted cannons means you don't have to worry about convergence at any range, and the .50s on the outside mean you have some cone of fire for those planes that are in close and are just a bit off your centerline.
I consider the Ki-61 cannons to have a pretty fast rate of fire.
You don't see it much in the Late War arena because it's outclassed in level speed by so many other planes, owing to the fact it has the same engine as the 109E.