Let us analyze the features provided by the two giants, some of them are close enough. The below table shows a high level comparison of the services provided.
Its very difficult to conclude AWS or Azure is best. It may be like comparing Lamborghini vs Ferrari!! LOL. Each has its on strength but choosing the right technology is purely based on the business requirements. If you are a strong lover of Microsoft Technologies or you already working with Microsoft Tools and IDE then you have a strong pull to Microsoft Azure than AWS. Anyways the choice is purely based on the Business needs and its case to case!!.