Were it not for the Mac OS, you would not be using Windows today. Were it not for Apple's original Apple I desktop, you would not be using a desktop today (nearly all previous desktop 'computers' were little more than enhanced game consoles). Were it not for OS X today, you would not be using Windows 7 (XP was really the best version of Windows until 7). Quite honestly, were it not for Apple, computer technology simply wouldn't be where it is today.
However, Gates was a marketing genius. He started with a cheaply-bought OS created by a fellow student and licensed it to IBM for their pending PC computer, conceived when someone realized that off-the-shelf components could build a simplified stand-alone computer. Interestingly, this concept arrived about 2 years after the original Apple i and about a year after the first retail Apple II hit the market. Because he managed to keep the licensing open and riding on IBM's apron strings, he managed to get a steel toe in the enterprise door that literally dragged Microsoft into desktop dominance.
So just because Microsoft practically owns the enterprise desktop market, it's no proof that they made the better contribution. You, yourself, said that Microsoft is always playing catch up, but it's not just on the consumer market. Were it not for Apple and Jobs' advances, we'd still be stuck in the 80s as far as desktop computing is concerned.
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