The downside of the cryptocurrency will be its volatility. The World can't have a currency with a value that changes from time to time. It will affect the Economy and that kind of currency will not stay long. I think this is the major downside of the cryptocurrency.
Volatility isn't permanent. One of the main factors contributing to it is distribution. Big currencies like the dollar are more stable because they're distributed among millions of people. At least 300 million people use the dollar every day. How many people own Bitcoins? It's hard to say but much less. How many people use Bitcoin every day? It would be great even if it was 3 million. If we went to 30 the volatility would be 10 times lower.