One nice thing about many of these apps is that you can do both. My wired cycling computer recently died when I stretched the cable during a bar retape, and I haven't replaced it yet. Instead I started using Map My Ride on my phone more regularly, but I don't look at it during the ride. I start the app at the beginning of the ride, zip the phone up in my Fuelbelt, and when the ride is over I stop the app and see how I did.

Having real-time data is great for pushing yourself in a workout, but it also turns every ride (at least for me) into a workout. Being in 'just ride' mode is nice, but since I'm going to have my phone with me anyway, I might as well have a record of the ride. Best of both worlds.