Watson APIs will be accessible - without the need for an application - as part of BlueMix (https://ace.ng.bluemix.net/ - the IBM PaaS/Heroku) in a couple of weeks. Stay posted!
I wouldn't choose Azure myself, and I would actively recommend against choosing it to others from what I have seen (unless you are building a solution on .NET/Windows, perhaps). I can't imagine that I'm alone.
[1] http://www.zdnet.com/microsofts-azure-virtual-machine-cloud-...
[2] http://azure.microsoft.com/blog/2013/02/24/windows-azure-ser...
[3] https://news.ycombinator.com/item?id=5266947
[4] http://www.thewhir.com/web-hosting-news/leap-day-glitch-caus...
[0] http://www.forbes.com/sites/georgeanders/2014/07/28/amazon-i...
I get the impression that Azure specifically as PaaS/IaaS, OTOH, is quite a bit less so. At least compared to AWS.