Google Analytics site speed data is only based on 1%[1] of your traffic while New Relic's Real User Monitoring aims to track all of your traffic. I'm sure that can lead to differences in accuracy.

(Disclosure: I used to work for New Relic)

[1] https://developers.google.com/analytics/devguides/collection...

Provided you have enough traffic, sampling shouldn't affect the results in any meaningful way.