Query execute slowly when changed compatibility Level of my database
I have recently seen this exact same problem with an upgrade from SQL Server 2008 R2 to SQL Server 2014 where a very small number of Stored Procedures (SPs) (approx 5 out of 3,000 ) performed worse in SQL 2014 Compatibility Level 120 than in SQL 2014 Compatibility Level 110 or in SQL  2008.

In SQL 2014 the Cardinality Estimator (CE) has changed which may impact how a SP performs in SQL 2014 Compatibility Level 120. 

There are a few possible solutions


Leave the SQL 2014 Database running in Compatibility Level 120 and add a dbcc Trace Flag to force SQL Server 2014 to use the prior CE &lt;-- I would not recommend this
Leave the SQL 2014 Database running in Compatibility Level 120 and Tempoarily add 

OPTION (QUERYTRACEON 9481)


to the offending SP to force just that SP to use the prior CE. The SP should now perform in Compatibility Level 120 as it did with Compatibility Level 110. &lt;-- I prefer this approach as your Database/System gains all of the other advantages of SQL 2014 while the "fix" only impacts the offending SP.

Irrespective of the approach I would then profile the execution plan/read/writes etc of the offending SP on a test system in SQL Server 2014 Compatibility Level 120 and rewrite the SP to cater for the new CE. 

Once tested and verified I would then apply to production.

Microsoft have a good article on the Cardinality Estimator changes in SQL 2014