Advantages to doing an initial instrument rating training in a Cirrus over a conventional aircraft?
There aren't any. Unless you are planning on purchasing a Cirrus, you'd just be burning money for no good reason by training in that. An instrument rating is an instrument rating regardless on what aircraft you train. What is important is the quality of the training, ground and flight. If you think about it, I am quite sure you can find better ways of spending the money you will save.