MS SQL Server CPU load goes up dramatically when turning on 2014 features by setting compatibility level
I would suspect the new cardinality estimator as a responsible for this behaviour, you can read up on it in the msdn article

It is clearly stated that the new cardinality estimator takes effect when you put the database in the new compatibility mode.


  Upgrade all existing databases to use the new cardinality estimator.
  To do this, use ALTER DATABASE Compatibility Level (Transact-SQL) to
  set the database compatibility level to 120 or higher.


There are trace flags that control this behavior.
If you want to use the new cardinality estimator when the database is in the old compatibility mode you can enable trace flag 2312
If you want to use the old cardinality estimator when the database is in the new compatibility mode you can enable trace flag 9481

If you can isolate the problematic query you could try to tune it so it performs well with the new cardinality estimator or if that doesn't work you can use the QUERYTRACEON keyword on that query only. That is also documented in the msdn link.

Also note that when, setting a trace flag you might need to use DBCC TRACEON (&lt;traceflag&gt;,-1) where the -1 sets it globally.