I use both Strava and Garmin Connect. Strava is for quick and dirty results and GC is deeper and more detailed. I don't race.

What Strava has that GC doesn't, is the ability to see what friends are doing and communicate with them in a central place. For instance, a riding buddy of mine recently moved 5 states away, and with Strava we can keep in touch on cycling, give each other some grief, that kind of stuff. I do segment my rides, but it's purely to track my own results and progress throughout the year. I see where you're coming from, but I don't think that's a reason to totally write it off.