In My opinion "The clock doesn't work at all".Because it is atleast shows a correct time at one point of time everyday.But where as the first clock will never show the exact timing...ISTN'T????
What about the one which loses a minute every day, since you can calculate how much shortfall there is and know the exact time everyday instead of having a stopped clock and not knowing the time at all.
The one which looses a minute every day works better. It shows time with error of maximum one minute. We can easily adjust one minute everyday....
On the other hand, the one which does not work at all is of no use. Its true that it shows exact time twice a day but how would we know that when it is showing exact time....