We're barely halfway through the month, and the world's two largest restaurant chains, Subway and McDonald's, have both made big surprise announcements.

McDonald's went first, abruptly naming Chris Kempczinski its new CEO, after the man he replaced, Steve Easterbrook, "violated company policy and demonstrated poor judgment involving a recent consensual relationship with an employee."

As I wrote at the time, I think the way McDonald's handled this surprising news was "an intriguing lesson in how to handle bad news and share it with the world."

Now, we turn to Subway, where a new CEO will take over Monday.

Both his background, and the difference between the McDonald's and Subway leadership transitions, are remarkable.

Meet and congratulate John Chidsey, the new CEO, who is best known as the former CEO of Burger King. He stepped down from that job nine years ago, when Burger King was acquired by 3G Capital, a multibillion-dollar investment firm.

Chidsey is the first permanent CEO of Subway who wasn't related to one of the founders, and I find his appointment fascinating. I'd love to sit down for interview with him and ask him things like:

What are his plans for the struggling Subway enterprise, which suffered through three years of record store closures?

How does he plan to work with franchisees, since he reportedly had a fraught relationship with Burger King franchisees during his time there?

What else has he been doing in the interim (besides investing and serving on boards, apparently), since he left Burger King in 2010?

I listened to an interview Chidsey gave in 2008, when he talked about how he likes to see job applicants who have had varied employment experiences, because they've been challenged and seen new ways of doing things.

Does he think his time away helped him in the same way?

But that interview isn't happening.

In fact, Subway apparently isn't setting up Chidsey to talk with anyone in the media, or offer anything beyond a 38-word quote in a press release announcing his appointment:

"I am honored to be joining such an iconic global brand, and I am most excited about the future of Subway. I look forward to learning from and working with the many constituents who have built this brand."

No offense, but it's not exactly illuminating. And that's precisely the point.

McDonald's is a $146 billion public company. Its stock skyrocketed while Easterbrook was in charge. It has to reveal reams of information to investors and the Securities and Exchange Commission, and answer all kinds of questions when its leadership changes.

Subway? It's still privately held -- divided equally, as far as we know, between its co-founder, Peter Buck, and the widow of its other co-founder, Elizabeth DeLuca.

Even its last permanent CEO, Suzanne Greco, who is the sister of co-founder Fred DeLuca, had no equity, according to reports.

So while Kempczinski takes over McDonald's under the watchful eye of executives, employees, franchisees, investors, and analysts, Chidsey will run Subway under less-visible circumstances.

It's a difference we've seen and written about many times.

Do the distractions of going public outweigh the benefits of raising money and sharing value? I'd love to ask Chidsey for his thoughts.