SQL 2016 Always Encrypted, options appear in one environment, not the other
I see this question is a few months old, but I wanted to tell you about a great update from Microsfot if you've missed the news.

On November 16, Microsoft announced the release of SQL Server 2016 SP1. Along with the normal things found in Service Pack releases, they also included CREATE OR REPLACE functionality. And, really important for your question, they've made quite a lot of the features that you can develop for available in editions other than Enterprise.

Most critical for you here is the availability of the Always Encrypted feature in SQL Server 2016 Standard and even Express starting in SP1 of SQL Server 2016.

You can read about that here on Microsoft's blog post.