I use both... I like my phone because it has the ability to record an elevation profile, route etc, and keeps a history of past rides... But, especially on long rides in remote areas, the battery can drain pretty quickly.

I use MapMyFitness that I keep in my trunk bag, and it displays the basics on my Pebble watch. I usually also have the Cateye computer on my bar whether I am using my phone or not. I initially did it for the redundancy, but now I am not really recording my totals, so it really just depends on my mood, and whether my phone is fully charged in deciding which to use. If I ever get my cadence sensor working right (magnet placement/crank to frame distance is making a reliable setup elusive), the bike computer will give me cadence, which I will check occasionally to keep me spinning...