There is no contest on who is the better brand, Coke wins hands down...even the word Coke, something we use to describe cola is their brand! How much more dominant can you get!.
Pepsi have by far the better drink which people far prefer, but Coca-Cola outsell Pepsi by stupid stupid amounts. That is ALL down to their brand power and horrendously amazing advertising, how on Earth has a soft drink company engrained themselves so much with Christmas is beyond me.
Great amount of credit needs to be given to the guys currently, and previously in charge of their image/marketing.
As for Pepsi, they've changed a fair amount through the years and will never the 'iconic' brand that Coca-Cola has, so personally I don't see the harm in their constant revamping of the brand. They have nothing timeless so there's no real harm with keeping up with trends for them. The damage to them was done years ago and is pretty much unfixable now.