Does a company have any advantages to choosing a fiscal year end of June 30 rather than a calendar year-end?

Yes they do.

For example.

If my business does most of its sales from October – March, and I offer a return policy, having a June year end would reduce the need for as many estimates as I would otherwise need to have.

Another advantage of a June 30 year-end is the potential reduction of audit, review or compilation fees due to the fact it's off season for CPA firms. And occasionally they pay a little more attention to you due to the lack of time constraints. Simple supply and demand here.