To my surprise i still have friends who don't know about the browser method of managing your gear in destiny. Most people are familiar and know about using the mobile app
iOS: https://goo.gl/QK1ZyN
Android: https://goo.gl/f5PE5g
Which was the fastest method, until bungie gave birth to this highly efficient browser method. If your not entirely sure if it's faster than using your app, then put this method to the test. Load a character and switch gear using your browser, then do the same using your mobile app. Once you've put it to the test let know how'd it go (-_^)d.
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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.