***** NOTE: take a look at this video, while not Azure Gov specific, it goes into much more depth on this topic: https://channel9.msdn.com/Series/SAIIK-SQL-Server-on-Azure-IaaS-Implementation-Kit/SAIIK-PaaS-vs-IaaS
I get asked this question frequently by customers. Figured I would share my thoughts on the topic with you guys, and some links to some helpful resources.
First thing you have to decide is Platform as a Service (PasS) or Infrastructure as a Service (IaaS). There is a great article with all the information that you need to make this decision here:https://azure.microsoft.com/en-us/documentation/articles/data-management-azure-sql-database-and-sql-server-iaas
If you choose PasS congratulations you are done!
If you choose IaaS you have to figure out your licensing model. Bring your own license (BYOL) or Pay as you go (PAYG). In general if you already have a purchased license that you can move then use BYOL, if you have to purchase a new license use PAYG. PAYG provides you much more flexibility to grow/shirk your investment as your needs change, additionally it requires no pre commitment. You can read more about the licensing here: http://azure.microsoft.com/en-us/pricing/licensing-faq.
Two tips here:
1) You CAN mix and match BYOL and PAYG in your environment
2) If you need to switch you will need to stand up a new VM and move your data over
If you are using IaaS use this doc to guide you through the best way to set everything up:
Double BONUS Tip:
If you are looking to migrate to SQL DB PasS check out this migration tool from George Huey: http://sqlazuremw.codeplex.com/