What's killing Microsoft is also mobile computing. If you've used Windows CE or one of its children prior to Windows Phone 7, you probably have said at some point that they deserved to lose that market. Unfortunately, that's the growth market, and Apple took the lead by being the first to bring the old capacitive screens to phones. Windows has spent and spent to get back into the market, but the damage is done, and the money is being wasted.
What will be killing Microsoft is Cloud. Yes, they have a cloud presence, but after years of licensing practices that users thought were confusing, problematic, and downright dishonest, they don't have the credibility to lead that market over Amazon, Google, and other heavy hitters, and there is a growing interest in small companies offering the same Cloud services, that don't have huge targets painted on their servers like the heavy hitters do.
Apple, by virtue of their glamorous perception, has been growing in the public view. In the early days, Jobs and his mindset of acting like a monopoly until it became reality nearly killed the company. They went to "underground" as a marketing campaign multiple times to keep their computers afloat, getting small pockets of strong support among unproductive people and artists. Then came the iPod and OSX. They jumped on a market that nobody dared invest in and established themselves there they was Band-Aid did bandages, to the point people thought any other mp3 player was a "knock off". They also solved the nagging issue of compatibility with the Windows world by letting the Open Source community do the hard work for them with a *nix base to OSX. When you throw in the iPhone and its early dominance, and the iPad's current early dominance, Apple has risen above Microsoft in company value, as far as Wall Street is concerned.
For all it's evil, Microsoft was never as bad as Apple about locking down its platform or restricting its users and customers. We thought this changed with OSX, but iOS brings it back with a vengeance. In the emerging markets, Google is the "white knight" to Apple's "black night" in this regard, even though Google has its own share of evil. Apple also lacks the vast cash reserves that Microsoft has spent to fight progress for a decade. It's no longer the fastest growing in the mobile market, and its Cloud presence is a joke. Apple did sweep the over $1k PC market, but most people are spending under $1k for their PC.
In short, Apple is doing well today, but it has positioned itself where it always positions itself - Overpriced, with an overinflated perception of quality, excessive restrictions on its users, and fighting against compatibility with the rest of the industry.
Unlike Balmer, Jobs does two things well. First, he sells. He is probably the greatest salesman to run a company since PT Barnum. He has developed a cult of personality that instantly translates to sales. Second, he dives in. The technology for the iPhone and iPad has been around for decades. Market experts said it wasn't viable even as people complained about why such things didn't exist. He listened to the people and invested his company's assets into it.
Unfortunately, Jobs isn't healthy. His health issues that don't bode well for him seeing another 20 years at the helm, and even 5 is suspect. We already see the stocks take a nosedive every time he sneezes or drives by a doctor, so the reality is there that the day he does quit or kick the bucket, Apple will redefine terminal velocity as its stock falls. The model he has structured is sustained only by his ability to convince people he has what everyone wants. Microsoft, for better or worse, made themselves necessary. Apple products, though, are immanently replaceable. iPhone held the market for a while, and iPad holds its market now because the alternative is seen as imitating rather than offering new value. That perception died with the iPhone with Android and maneuvering by Google. The iPad won't magically fare better in the long run.
And then there's the stock value. It's huge for what little Apple actually owns by comparison. The company's P/E is 15.5, which is relatively moderate, and it's still faltering in the business sector. All this tells me that the stock is overinflated. Much like his products, Jobs has sold his company well, and the stock has risen accordingly.
Apple isn't taking Microsoft's place. It is, however, taking back the place it occupied in the late 1970's. If anyone, Google is the new Microsoft, reaching to the masses and to businesses rather than trying to present their products as status symbols.