SQL 2012 is out of support and has been for over a year. 2014 will be out of support next year. Upgrading to either of them at this point in time is a bad idea, and there are many compelling features in 2016/2016 (Query Store!)
I recommend that you speak to those vendors about getting their apps certified on 2017 (or see if they're happy with them running on 2017 in an older compat level), and upgrade to 2017.
The Extended Support Date for SQL Server 2012 SP4 is 2022... https://support.microsoft.com/en-gb/lifecycle/search?alpha=sql%20server%202012
Same date for SQL 2014 SP2
If you want to be pedantic...
SQL 2012 is out of mainstream support (so if you want support you have to pay for it, no non-security patches will be available, and you have to have an agreement to get this). SQL 2014 will be out of mainstream support next year (so if you want support after that you'll have to pay for it, etc)
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability
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