Azure - Why Pay More

I have worked with several customers on cost optimization of their cloud spending. Below are some tips that could help you with cloud saving.

1. Leverage the elasticity nature of the cloud. You can certainly save money by deploying resources to Azure, but only if you take advantage of the features of the platform that allow you to scale up VM during peak hours and then scale down or turn off VM during off hours. If you just move a VM from on-premises to Azure and then leave it running 24x7, chances are pretty good that you will end up actually paying more than if you had left it on-premises.
2. Majority of the cloud spending is on Compute, typically 80% of your spending. Make sure your shut down VMs that are not in use (could consider Azure dev/test lab for easy automation). I have also found this automation script quite handy.  Also be careful about the difference between Stopped and Stopped (Deallocated). One charged compute cost, the other not. I know this is confusing but see detail explanation here.
3.  Leverage Enterprise MSDN Dev/Test offering. Enterprise Agreement customers have a great way to run their development and testing workloads on Azure where it has special low rate for Windows Virtual machines, cloud services, HDInsight and web app. This is ideal for team running pre-production workload and drawn down from the EA monetary commit in one bill. Separately, each active Visual Studio subscriber also can set up one separate individual Azure subscription with a monthly credit, which is ideal for light development and testing workloads, experimentation with Azure services, learning, prototyping, and proofs of concept. These monthly Azure credits for Visual Studio subscribers are unrelated to Enterprise Dev/Test subscriptions and only suitable for individual use.
4. Leverage Microsoft Hybrid User Benefit  (aka BYOL for Windows Server): With the Azure Hybrid Use Benefit, you can use on-premises Windows Server licenses that include Software Assurance to earn special pricing (base compute rate) for new Windows Server virtual machines in Azure.  
5. What you see on the official Azure price calculator is the retail price. Your Azure Enterprise Agreement (EA) normally provides certain level of discount that makes big difference in your discounted cost. Keep in mind discounts are going to vary a lot, depending on your commitment tier. Always check with your EA admin for the right price sheet in order to estimate the project cost.

Hope the above information helps.