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Clearly they are, but it's not as if Pepsi is badly flailing or dropping off the map.  They just have a lot of subbrands.

Pepsi as a company is much larger.

I am 100% certain that Pepsico Executives are not happy about this at all, and are probably making plans as we speak, for significant changes.  Dr. Pepper is a tiny upstart, this is a huge problem for Pepsi.

It's a kind of bragging point, yes, and dropping from #1 to #2 is huge because of retailers like Costco.  The Pepsi folks won't like this, but I don't guess they are panicking over it. 

Fired?  Maybe so.  I was on the edges of some marketing stuff, and folks were indeed worried about slipping from #1 to #2.  I thought there was less concern if #2 slid to $3, but I could be wrong.  I don't think anyone would have been fired where I worked, but their careers may have gone south.  I was there when Pampers slid to #2, in part because we also had Luvs at the time.  As I say, I was on the fringe, but I was not aware of any panicking.

It reminds me of the Ford-Chevy light truck story, Ford leads Chevy comfortably, but if you add GMC, GM makes more light trucks.  Does GM care that their share is split?

Is Pepsi that worried so long as their sugar free brands are growing faster? 

I just looked at the five year stock chart for both companie, which of course is a gross check, and oddly their stock returns are almost identical over that period.  It could be Pepsi has made a strategic choice to emphasize sugar free perhaps understanding Pepsi would slide in share, I don't know.  And of course, maybe they react with more marketing and recover the #2 spot fairly quickly, or decide it's not worth it.

Should GM stop marketing GMC trucks to perhaps be able to claim the #1 spot?  I doubt it.  I think some folks prefer GMC to Chevy for whatever reason.

It's kind of funny, our "core brand" originally was soap, Ivory soap (and before that candles).  It was long since of course allowed to slide.  We had a large coffee brand for a while, it was sold.  We had Duncan Hinds, also sold.  We owned one of the largest acerages of forest land for a while, that was sold. 
Maybe that's why that outfit has been around so long.

I think Tide took over cica 1950, it dates from 1946 as I recall.  It coincided with new washing machines coming on line, and some brilliant marketer managed to put small boxes of Tide in each new machine. 

But it well could be that Pepsi is firing marketers and planning a counterattack.  Or maybe they are just focused on sugar free as a better profit center.

To be clear, I am corrected that Dr. Pepper the brand has edged Pepsi, I was wrong on that point.