SQL Server 2016 Standard or Enterprise for SharePoint 2016
Are there any disadvantages of going for SQL server standard edition
  instead of enterprise


The disadvantage is you can't use enterprise features, like AlwaysOn AG among others (see below). If you aren't going to use these features, then you don't need Enterprise generally speaking. The advantage is you'd save some money. Both are licensed per core, and enterprise costs more per core.... like 4X more than standard. 

Here are features that come in Enterprise that don't come in Standard:


Unlimited memory (max of OS)
Online Page restore
Online index rebuilds
Mirrored backups
Automatic tuning
Transparent database encryption
Parallel index operations
etc...


See the data sheets, and the full comparisons for the differences. Generally speaking, unless you really need those enterprise features, I'd would opt for standard for the HUGE cost savings.

Microsoft also has a guide to help you decide which one you need.