According to this article on Market Realist, Microsoft Azure is projected to reach an annual run rate of $8 billion in 2016 compared to Amazon's AWS run rate of $7 billion in 2015. They are saying Microsoft will begin to catch to up to Amazon because of their long history of selling enterprise software to big companies.
I tend to agree that Microsoft along with others like Oracle and IBM will continue to make inroads on Amazon's dominant market position because of their customer relationships as well as the absolutely HUGE investments each of them are pouring into this race to catch up to the leader.
Although Amazon has a huge lead on each of them, these other competitors have huge cash cow businesses that will allow them to make large strides in closing the gap. Amazon will be able to rely on scale at least for the next year or two, but eventually these players will catch up and the then The Cloud Wars will really start beginning.