Been there, done that (ie. used a phone).
Virtually no phones now have ANT+ connectivity. Using BT to connect to sensors is a giant PITA because it's a one to one connection. ANT+ is a one to many connection which allows you to have more than one computer listening if you need redundancy (say if you're having a problem). I've also had issues with some of the metrics - for example I used to use Cyclemeter but found that the caloric measurement was wildly off (like by almost 100%). Maybe they've fixed that, but I moved on. I ride with a full sensor set up with HRM, Power Meter, speed sensor. A speed sensor is much more accurate than is GPS for distance and speed. GPS is not as accurate as most people perceive it to be.
Problems with hardware that I've had are that the phones often have trouble with heat in direct strong sunlight while trying to act as a bike computer. They are built to be in your pocket with a low duty cycle. They are not built to be 100% of the time on a hot day sitting on your handlebar in bright sunlight for hours on end. They also are not anywhere near as rugged as a bike computer is to dropping or crashing.
Then there is cost - a bike computer costs anywhere from $100 to $500. You're smartphone starts at $600 and goes to $1200. That's cost in the wrong place, IMO.
So my experience has been that the metrics are not as good, the phone is not as robust in environmental specs, and it's not as durable. Basically, it's just not the right tool for the job. Yes it will work, but I guess I'd rather not put a computer on my bars that costs twice as much as a bike computer and isn't as good.
J.