Even in such a vague form, this is a touch sensationalist. The impact of 'the one that wins' may be negligible. There also may be no winner.
Effectively, these two companies embody fairly different points on the spectrum of shareholder control: Google being effectively a public closely-held company; Apple being a public widely-held company. True, Google has millions of shareholders, but the _control_ is closely held, hence why I am using that term.
The control that shareholders (and activists and raiders) can have on Apple is significantly different than on Google. And that is what the article is about.
Over time, the market could adjust from the Apple model (which is the status quo in public companies) to the Google model. The implications are tremendous, as the idea of a public company that is closely-held over the long term hasn't really been done before.