Gremlin has a natural compilation to the common distributed vertex-centric computing model (bulk synchronous parallel for graphs). Thus, Gremlin works for both OLTP (graph databases) and OLAP (graph processors). The Apache distribution provides OLAP connectivity to Apache Hadoop, Spark, and Giraph.
Gremlin supports both imperative path expressions and declarative pattern matching.
Gremlin can be embedded in any host language. No "fat string" with result set. The user's database query code and data manipulation code are in the same language. There exists Gremlin-Java8, Gremlin-Groovy, Gremlin-Scala, Gremlin-Clojure, Gremlin-PHP, etc.
Gremlin is Turing Complete. Most any complex enough language is. However, Gremlin is related to a Turing Machine by a very simply mapping.
See http://arxiv.org/abs/1508.03843 for detailed specifics of the aforementioned benefits.