A notable difference is that Azure file shares have a 5 TB limit for the whole share, and a 1 TB limit on the size of any given file [1], while EFS has no limit on the size of the file system, and a 52 TB limit on the size of any given file. [2]
Disclosure, work for AWS.
[1] https://azure.microsoft.com/en-us/documentation/articles/sto...