In most situations, competition is a great thing. It drives companies to innovate and produce better products and services. While that will certainly happen with their respective mobile operating systems in this situation, I believe these are two companies that would be much stronger working together.
Google and Apple are good at very different things. Gruber nails it when he says:
No better comparison of the cultural differences between Google and Apple than to compare Google Docs and iWork. iWork has no form of cloud based syncing or collaboration; the appeal of the apps (both on the Mac and iPad) is that it helps you create beautiful documents. Google Docs is all about cloud-based syncing and collaboration; its example documents are downright homely.Google is great at building services that scale. Gmail, Google Docs, and Google Maps are all great services, usually with simple and effective interfaces. Apple is great at creating intuitive user interfaces and well engineered hardware. As an end user, I want my services provided by Google on hardware built by Apple.
More specifically, I want my web user interfaces built by Google, and my native applications built by Apple. I enjoy the close integration I have on my iPhone between the Calendar, Mail, and Contact applications and Google Apps (which is ironically made possible by Microsoft's ActiveSync). I like Google's web interface to Gmail and Calendar. I want them both, and I want them to work together.
In my ideal world, Google would provide a service interface for these services, and a generic web interface that is accessible anywhere, on any (modern) browser. Apple (and others) would provide native applications that utilize these services. I want to be able to access my data using either the browser (provided by Google) or a native app (by Apple) on either my iPhone or MacBook. I wish the Address Book application on my MacBook worked as well with Gmail as the Contacts app does on my iPhone.
It should work this way across all services. iWork should be able to store and edit files on Google Docs, which could then be edited using the web interface as well. Everything lives in the cloud, with the ability to cache local copies with the native applications (or advanced browsers).
Unfortunately, it looks like Apple and Google are moving farther apart, instead of closer together. It is clear that Google first 'invaded' Apple's space with Android, but Apple is certainly a company that holds grudges and is very aggressive. Adobe knows this all too well.
As an end user, I'm afraid this is one area where competition may not produce the best result, but who knows. Neither Google nor Apple are going away anytime soon, and they may both surprise us with what they do. Let's just hope it is about creating better products instead of damaging the competition.