This is a tricky question because it depends on what you mean by "bigger."

* Size: Stars are much, much larger than the Moon. Even the smallest star is many times bigger than our Moon.

* Apparent Size: The Moon appears larger in our sky than any star. This is because the Moon is much closer to Earth than any star.

So, the Moon is bigger in the sense that it appears larger in our sky, but stars are much larger in actual size.