Doesn't the outcome of testing which method is faster depend a lot on where your computer is located in respect to where you're gaming? I personally don't game with a laptop next to me and my PC is in another room so for me the app is a much faster choice.
I usually try to have my laptop next to me when I'm playing but sometimes I'm too lazy to get it and boot it up and sometimes I leave it at work. In those cases I use the browser on my phone and the Bungie website over the app still. The app is great for browsing the forums and checking stats and things, but using the browser on your phone and going to the website to manage gear is way better.
Ill have to give the mobile browser option a try...i usually leave my laptop in my office upstairs so when i game it's not close by. But the app is a pain to manage gear so maybe ill prefer the browser method! Cheers