Amazon Cloudsearch can be suitable for some queries that require fast data. For example, in our case, we used CloudSearch, in a tool called Global Search. That will search everything like names, emails and a lot of stuff in our application. If you want fast data and you have a simple query, Global Search isn't appropriate for you.
To better serve their consumers, businesses that often interact with those clients who rely on Microsoft's software products may consider migrating to Azure. This program would be useful in any installation of a Microsoft product or suite that necessitates a test of the target environment. It is simple to maintain and implement, making it an ideal IT backbone. If a client doesn't have any use for this particular instrument, it's not going to be of any benefit to them.
I didn't investigate the best alternatives to CloudSearch, but did help with implementing this feature in our application. But from what i tested and used - Cloudsearch is very fast to get queries. Some negative points can be the time to implement this and some configurations that can be tricky.
They both are great tools and provide the services they have implemented. They are two competing companies that have different cultures and forward mission agendas. I would say Azure is a little easier to support through their user interface for the IT support side of things. Both tools are useful and have their own strength and weakness. If you're a dynamic company with a multitude of customers then both are a required tool to have.