Intel vs ARM will turn out to be a more exciting battle as current ARM ecosystem partners come under competition with ARM entering new markets (think nVIDIA's dilemma as ARM pushes Mali) and if Intel gets an ecosystem partner or two.
Well, THREE x86 players if you want to count them all; people forget about VIA. But their market share is pretty forgettable.
There are quite a few embedded MIPS processors out there, so taking all those MIPS sockets is not an insignificant goal. The fact that Microchip, one of the big players in the market for 8 and 16-bit embedded processors, went to MIPS for their 32 bit product can't be ignored either.