The answer is 2: the smaller hospital. The Law of Large Numbers says:
The more people we survey, the more accurate the result.
Larger samples are better.
In this case, the number of children born each day is a random sample of the number of children born in a year. There is much more deviation in a small (daily, in this case) sample than over an entire year. Similarly, there will be more deviation in a sample of size 15 than in one of size 45. Even though both hospitals will have about 50% girls over the year, the smaller hospital will have more days in which the number is higher than 60% (and more days when it is less than 40%). (Consider the extreme case of a hospital that has one baby a day. Every day will be either more than 60% girls (one) or less than 40% girls (zero).
People commonly and mistakenly believe that even very small samples will have the same composition as large ones. Remember this next time someone uses a small survey sample to "prove" something -- the results may be invalid!