It does basically boil down to what you are most comfortable with. Take, for example, I started diving with a "J" valve. I'm not so old that we didn't have depth gauges yet, but I did use both with the "J" operating as my trusty back up. I never once used the J-valve to inform me I was low air but it was there ready to be called on if needed. After the demise of my faithful valve came very easy to use bottom timers from Oceanic. So now I was using my depth gauge, a bottom timer but still kept and used my watch as a back up as well. But, I quickly got to the point that I never used my watch, only wearing it again as that trusty back up.
When I purchased my first "hockey puck" dive computer, computers were far from new. The Edge, Skinny Dipper and such had been around but out of my price range for a while. I had my computer in the same wrist boot my bottom timer had been in but still left my console with depth gauge in place. As expected, I found myself using that depth gauge less and less, eventually swapping the gauge to the wrist and the computer into the console. After while I got tired of using the wrist boot and would simple keep the depth gauge capsule in my bcd pocket. That trusted back up again.
Then came my time at Sherwood Scuba and the Wisdom. While my Wisdom has never failed me, I was the person in charge of dealing with all those that did have issues. I saw enough of them come across my work bench early on in that computer's existance that my trusty "hockey puck" was always in my bcd pocket, just in case. In time I came to realize that I could trust my air integrated dive computer and began leaving my old computer at home.
All in all, I found over 30+ years of my gear evolving that not once have I ever used my trusty "back-up" item, but for my own piece of mind I was always happy it was there.