Paradox of watches

We can agree that the best of two watches is the one that most often indicates the right time, right?

Suppose, then, that we must choose between two clocks, one delaying one minute a day, while the other does not work. Which one should we accept?

By common sense, we should choose the one that delays a minute a day. But to keep our agreement, we would have to choose the one that doesn't work. Why?

The clock that is delayed one minute a day, once right, will have to be delayed twelve hours or 720 minutes before setting the right time again. And if it is only a minute late, it will take 720 days to delay 720 minutes.

In other words, it will be right approximately once every two years. On the other hand, the clock that is stopped sets the right time twice each day.