"Dropbox, which is increasingly competing with Microsoft and Google as well as fellow startup Box in the fast-growing field of cloud storage," This implicitly (if not explicitly) reverses the actuality, which is really: "Dropbox, which is increasingly facing competition from Microsoft and Google as well as fellow startup Box in the fast-growing field of cloud storage," They do a better job later on with, "Those featu…
Since you're nitpicking, I'll just point out that both formulations actually have the same meaning. There's nothing (not even an implication) in the first quoted sentence that suggests that Dropbox is younger than its competitors. 'Competing with' and 'facing competition from' are exact equivalents.
And "Competing with" all are on equal basis.