Actually, I think Samsung SIII's worldwide have sold more than the iphone 5 worldwide.
Apple plays in the high-end market, and they do not have the ubiquitous distribution that the SIII has. Apple claims they are not after marketshare, and the stats that I have seen demonstrate this. They make a TON of profits (the point of most businesses, esp publicly traded ones), but they do not have the largest marketshare, nor do they sell the most units.
The route to world domination that both companies are taking have yet to be proven wrong or right. Samsung: sell the most phones, and you have the foundation for continued money. You get economy of scale, phone ecosystem lockin with accessories and apps, and you can make boatloads of profits b/c everyone has your phone everywhere, at a price that others can't match. This is the traditional way of doing business. I think that this model has the most growth potential. Outside of the ipod, Apple does not have a product that enjoys world domination. The masses matter, and as a luxury purveyor, experience shows that luxury brands do not enjoy world domination. They enjoy a fine good life, and one that I'd trade mine for, but not world domination that so many people think is necessary to validate that one company "wins" over another.
Apple: if you make the best product, it'll eventually win out in the marketplace, regardless of the price. As long as you don't make it 100 times the price of the competitor, then people will come up with the money to buy your product (and hand you huge profits per phone sold). You just have to make sure that your product really stands out. This way, the cream rises to the top, and eventually you'll reach a huge marketshare, and make even huger profits. Quality trumps all, more than marketshare, b/c if it's high enough quality,huge marketshare is an inevitable byproduct. The price sensitivity of consumers isn't a huge concern.
A couple of problems with this approach: people are always price sensitive, even rich people. There are many rich people who still want value and retain cheapskate mentalities. People want a deal. It's human nature and you can't get rid of it. Second, it's getting harder and harder to justify value in the tech world as hardware components are virtually identical now, and it's just inevitable that the competition reaches parity over time in the software segment. People copy, people combine, and true gamechanging originality is not confined to one company for very long. It's a social world more than ever, and no one has a monopoly on innovation. Heck, I'd wager HEAVILY that Google is the company who is doing the most innovating. They truly revolutionized search, The maps, streetview, the self-driving cars (they really work well). These are total gamechangers. Hinging on you being able to one-up everyone else is a hard act to keep up. It's just easier to bring someone down than to stay up on top.
You're seeing the limits now of Apple's strategy. People are seeing Apple's products as nice and slick, and maybe slicker, but not slick enough to pay alot more for. One could argue that much of Apple's advantage is just more refined physical design, which when applied at the population level, most people don't care THAT much about. Those who care that much will again be a minority of the market.
Android, which I HATED, in every way shape and form--the cold, robotic look, the nonsensical back button, the ugly handsets, the ugly crashing apps, the poorer quality screens, etc have all been fixed. All. And it's still way cheaper with way more choice.
As much as I hate to say it, Android is not inferior to iOS any longer, and they have reached parity. yet Android is cheaper, both the software and hardware. There is a reason why Android has accelerating momentum and marketshare. Regardless of how people try to spin it, having marketshare can ONLY be a good thing and from such a foundation lots of things can be launched to solidify and grow a platform. Even if you can grant that iOS and Android are equivalent, when you factor in the value proposition, Android eeks out ahead and the masses appear to be realizing that. Yes, Android got its start b/c the phone companies wanted more control and pushed Android. But eventually quality does matter, and Android to its credit is now a quality prpoduct and stands on its own two feet. Android gambled with the lets gain marketshare first with a good-enough albeit flea market feel, and then refine it later. That gameplan looks like it is working.