I run Strava and yes I like it but I don't take it too seriously. I like seeing how well I did on a particular leg though. It motivates me to push harder; and no, I don't try to "compete" against other riders but I do like to see how I stack up.
It's fun for groups to as a bunch of folks at work have a work group set up and it provides a fun venue to see who did the coolest ride over the weekend replete with photos of said event. Pretty fun in that regard.
I have found that the numbers posted by Strava need to be taken with a grain of salt though. I've made the mistake of not stopping my ride, hopping in the car and driving around town. WOW!! My average speed miraculously improved!! ROFL!