First off, digital clocks are actually considered preferred equipment in the USCF. In events where you bring your own clock, Black ordinarily has the right to use his clock, but if White has a digital and Black has an analog, White can insist on using the digital. So you've got nothing to complain about.
I've never quite understood why they can't make an analog clock that gives you an exact start point. (At least when you start on the hour.) Of course, accuracy to the millisecond is less important when playing G/60 or longer.
And a final point: How do you know your digital clock is really accurate to the millisecond? I used to have a digital watch that would lose two seconds per day.
digital clocks are precise and everyone has the same time to the last second.
I've noticed that some analog chess clocks vary in speed and in addition to that some might set it to a second off so that the two opponents do not have the same time 100%. digital clock eliminates human error.
having 10 millisecond more than your opponent is an advantage.
in my opinion since time precision is so important analog chess clocks should be sent to museum of chess.
the only thing about digital clocks is that they have to be made easier to set and easier to give a player a minut extra.