Ingredients for SQL Server Version decision
The is some information directly from MS that you might find useful: Breaking Changes to Database Engine Features in SQL Server 2016 and Discontinued Database Engine Functionality in SQL Server 2016, which indicate that officially there is very little by way of breaking changes. Those pages link to similar information about older versions too.

As a general rule I recommend going for the latest version for new installations once that version has been released long enough for any major bugs to have been found by someone else and fixed by MS, and SQL2016 had a large enough beta release that anything major should have been found already. But I would also recommend a full regression check of the applications to cover the possibility of:


reliance in your application on undocumented/undefined behaviour that may differ in the newer version: changes to officially undefined behaviour won't be listed in places like the pages linked to above.
performance issues due to changes in the query planner: the new carnality estimation method in 2014 generally lead to noticeable improvements but in a some use cases they had the opposite effect and hints are needed to push the query planner back towards the optimal plan, I'm not aware of such a significant change in that area in SQL2016 but there will no doubt be smaller changes that could have a detrimental effect for a minority of queries/statements.
new and interesting bugs as yet undiscovered.


As is sounds like you have recently performed a large scale regression test, you might not be able to justify (to the business) doing so again this soon in which case sticking with 2014 would be the safer option.