Spark 2.0 provides native window functions (SPARK-8641) and features some additional improvements in parsing and much better SQL 2003 compliance so it is significantly less dependent on Hive to achieve core funcionality and because of that HiveContext (SparkSession with Hive support) seems to be slightly less important.
Spark < 2.0
Obviously if you want to work with Hive you have to use HiveContext. Beyond that the biggest difference as for now (Spark 1.5) is a support for window functions and ability to access Hive UDFs.
Generally speaking window functions are a pretty cool feature and can be used to solve quite complex problems in a concise way without going back and forth between RDDs and DataFrames. Performance is still far from optimal especially without PARTITION BY clause but it is really nothing Spark specific.
Regarding Hive UDFs it is not a serious issue now, but before Spark 1.5 many SQL functions have been expressed using Hive UDFs and required HiveContext to work.
HiveContext also provides more robust SQL parser.