Marriott LAX vs Renaissance LAX
Data points: Mattress runs to Renaissance (September 2013, December 2015) and Marriott (December 2014)
Rooms: Renaissance rooms are just a touch larger and the property is a little bit more modern.
Concierge Lounge: Renaissance has the better view of LAX north runway traffic; both lounges are/were busy in the mornings; However, Ren's CL closes on Friday morning while Marriott's CL is open daily from 6 to 9 AM. Renaissance gives you a coupon for (continental) breakfast at their restaurant on weekends.
Fitness Facilities: Marriott's pool is bigger and better. Ren's fitness area is smaller but less contentious.
Airport Shuttle: I don't have this first hand but my colleagues tell me that the Ren's is better.
Good luck!
David