The biggest issue on a phone isnt even that the screen is smaller, it's that typing is not possible. A phone user is hunting and pecking whether with a physical or on-screen keyboard, so they will be entering characters slowly and hoping to find at match without entering the entire string. SOME users on a PC will be doing the same, and the same response is appropriate in any case of a slow typer - use all that idle time to search and display possible matches.
But when you have fast input coming in you should NEVER be interrupting that to search and display possible hits - that is counterproductive on any platform. (Even on a phone if someone can somehow send the input fast enough the same thing would apply.) The computer in that case should simply keep listening to the input. If the user hits mod4-firefox-<enter> at a decent pace without pause, there doesnt need to be any sort of GUI update for it at all, the only response needed is to launch firefox.