My interview process was a bit unique due to the fact that I interviewed for two separate positions with the company, one in Portland and one in San Francisco. Both followed a similar format of a preliminary phone screening by an in-house recruiter, followed by a 30-45 min phone interview with the hiring manager. The next step in the process was a series of one on one video conference interviews which lasted about three hours and consisted of 4-5 stakeholders. For my first position, this was also followed up by an on-site interview that followed the same format, only held in person. By the time I got through all this for the second position, I think I had spoken to just about everyone related to the role so no second on-site was required.
From an impressions perspective, New Relic exudes energy. By the time I got to the final interview I was under the impression that personality fit was the main focus. Competencies and experience was established in the 2nd and 3rd interview. In any event, I think folks who are really comfortable being alert, aware, and enthusiastic really have an edge in the process. It's worth reiterating that passion goes a long way.