Um... no, unless one takes over or they merge together, but I doubt that will happen, oooooor one of them falls, then the war will end, but I doubt it ever will. As long as there's 2 (3 if you count Linux) operating systems, there will always be a rivalry.
The thing is; that the motherboard chipset's of Mac's are the same as PC's except that Mac hardware is specially selected to work with OS X. Other PC's however do not have as stringent hardware portfolio's as Apple computers and this is why there are a variety of hardware set-ups and chipsets and a variety of OEM's that provide them. Windows is designed for a very large range of hardware and also OEM's deal with this range too; this does mean less consistent quality on the software-OS level for PC's than Mac's. PC OEM's are also notorious for installing bloatware and other un-neccessary proprietary software onto their systems which often cause instability for Windows (which has enough to deal with as it is).
Personally I choose generic PC's rather than Mac's because I can have more freedom over customizability - however this may be at the expense of long-term stability. Thus I do not think you could say its a "Mac vs PC" rivalry; its more of a case of Mac Vs Lots of differing PC OEM's. These OEM's seem unlikely to invest in making their own OS and their own hardware portfolio to monopolise around that; therefore its really a case of Apple Vs rest of the world (remembering of course that Windows can also run on a Mac).