It isn't that Bitcoin solves a different problem it is that is solves it better.

How many merchants accept Bitcoin, how many accept Doge?
How many well run, highly capitalized solution providers like BitPay are building infrastructure around Bitcoin?  How many around doge?

There is something called the network effect and no passing a few pennies between users isn't a network effect.  Bitcoin is still in the infancy but the number of merchants willing to accept it is growing.  As long as it is growing the network effect will grow with it.  When an Overstock, Wordpress, or even Kongregate starts accepting Doge you might have a point.

Your logical fallacy would be like me inventing a totally incompatible cellphone called a dogephone and this dogephone could only be used to call other people who have dogephones.  Right now 99.99999999999999999% of the people on the planet have no interest in getting a dogephone because their cellphone works just fine.  When you point that out to me I say "what problem does a cellphone solve that Dogephone does not?"