NewRelic gives you mainly a predefined set of metrics, where you just have to install the agent to get them. Then. There's an additional module where you can send your own set of metrics and display them.
Statsd on the contrary is 'only' a tool to collect and then display metrics. You have to define everything you eant to measure yourself (or use plugins to your app).
So these two are definitely related, but better used for different (although overlapping) jobs.
