We took a Lyft since there's just two of us, no kids/car seats etc... and minimal luggage. Anything more than that, it's probably more economical to take a shuttle. Also we arrived during rush hour and it was a LOOOONG trip.
If this is your first time flying into LAX - FYI you have to take a transport bus from the terminal to a parking/pickup lot for taxis, shuttles and standard ride shares (I think private car service and maybe Uber Black are allowed into the terminal, but that's it).