I don't think anyone will say that the turnaround at Gap (NYSE:GPS) is working very well. Plenty of data shows that the company has struggled to find the sweet spot for sales growth. It's arguably a more financially secure company today than it was five years ago, but declining growth in same-store sales remains a problem.

It's tough to turn around a big company like this when you're being attacked from all directions. American Eagle (NASDAQ:AEOS), Abercrombie & Fitch (NYSE:ANF), and Aeropostale (NYSE:ARO) really resonate with customers, and have all performed well over the same time period.

So with the leveraged-buyout craze potentially turning into a feeding frenzy, is now the time to get the deal done while there's capital flowing and plenty of incentive for private equity to use it? Or is it better for management to give it the old college try again and stay public? Maybe it will be in a different form, but it would certainly be under the watchful eye of public shareholders.

That's what Fools will be dueling about over the next few pages. Anders Bylund says it's time to gather the shares, sell them to the highest bidder, and fix the problem in private. Rick Munarriz says no way: Shareholders would be better served by staying in the public eye and finding a much-needed visionary CEO.

So with that, it's time to these Fools to roll up their sleeves and get busy. And at the end, we need your votes to decide the winner.

Fool on!

Retail editor and Inside Value team member David Meier is ranked 456 out of 21,135 participants in CAPS and does not own shares in any of the companies mentioned. You can view his TMF profile here. The Fool takes its disclosure policy very seriously.

Gap is both a Motley Fool Inside Value and a Motley Fool Stock Advisor selection. American Eagle is also a Stock Advisor pick.