Is the size of a penny important?

Answer 1

Not directly, but US Large Cents were discontinued in 1857 so the size is important in the sense that a large US cent is over 150 years old and thus is likely to be scarcer than a modern small cent.

But as the saying goes, "It's not that simple". Some Large Cents were made in quantity and some small cents were only minted in small numbers, so some small cents (e.g. an 1877 Indian head cent or a 1909-S VDB Lincoln cent) can be worth a lot more than a common-date Large Cent.