Lots of small SQL statements in SQL Server and measuring network time between DB and Client I am load testing an application and it appears from New Relic that each transaction executes a significant number SQL statements (approx 250). As we scale up, the service that makes these calls appears to degrade; however New Relic is a bit unclear as to why this is as it does not account for all the time (just the SQL execution time). 

In Oracle I would be able to run a trace which would show the latency of the network round trips associated with execution of each SQL statement. Is there an equivalent set of SQL Profiler (or similar) metrics that will help me trace the time between the client service issuing the SQL request and it receiving the response?
It's been a while since my Oracle days but IIRC, that's at the Ora net layer so the equivalent in SQL Server will be ODBC or .NET provider layer. Profiler is a client tool that calls SQL Trace in the server. It can't capture client-side network stats so if you're trying to measure client/server network latency, it won't help you. 

You can track ODBC clients statistics by enabling it from the data source administrator. See https://msdn.microsoft.com/en-us/library/ms131411.aspx for details. 

For .NET provider statistics see https://msdn.microsoft.com/en-us/library/7h2ahss8(v=vs.110).aspx

Jes has a nice blog about enabling it from SSMS if you are testing specific queries, see https://www.brentozar.com/archive/2012/12/sql-server-management-studio-include-client-statistics-button/

If you really want to get details, there are a bunch of other tools with varying levels of detail and abilities like netmon, tcping, tracert, etc... but they'll typically require manual correlation so I won't start with this.