AMD was officially the first CPU manufacturer to produce a 64-bit CPU.
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When Intel released the Pentium II which had a whole new instruction set, AMD had to work to catch up and release a comparable product. The same happened for the Pentium III and IV eras.
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But in the end, the debate comes down to basically one simple fact. Intel is the one who essentially set forth the basic standards for x86 CPUs and have been the innovators for improving this technology. While AMD worked on creating supposedly "faster" CPUs, Intel has always worked towards advancing technology.
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And that's why I have always chosen Intel. I'd rather have superior technology rather than gaining a few microseconds here and there when I'm having my computer perform CPU intensive functions.
Okay, I don't normally do this but I couldn't let it pass. A quick Wikipedia search reveals that 64 bit CPUs have existed since the 1960s. While MAYBE Intel is the one that came up with them (they were formed in 1968), I'm pretty sure you're referring to the relatively new 64-bit architecture. Either way, 64 doesn't matter one bit unless you're actually using a 64-bit operating system (so keep that in mind BlackIrish). Why pay for something you won't use (unless you have to get the 64-bit processor to get the better 32-bit speed)?
EDIT: Whoops. You said that AMD came up with 64-processors and then I went on a rant about Intel. AMD was formed in 1969, so again, the point still stands and I doubt they were literally the first to come up with 64 bit processors.
A whole new instruction set doesn't mean much. New is not necessarily better. Yeah Intel came up with the x86 architecture, but I'd blame its popularity not on superiority but on software (ie Windows). AMD was playing catch up not because the new instruction sets were "OMG AMAZING" but maybe because software started supporting these new instructions and if AMD didn't add support for them people would start complaining that their algorithms run "slow" when it runs "fast" on the Intel machine. That being said, yes Intel has come up with some useful / cool things (SSE, MMX).
As for AMD working towards "faster" CPUs... does anyone remember a few years ago when Intel was pimpin' their multigigahertz processors and pulling the whole "higher clock speed = faster" thing? AMD instead had MUCH lower clock speeds and then comparable performance to one of Intel's much higher clocked chip. AMD eventually started to advertise their processors as being X gigahertz but then labeling it as (for example) "3200+" to show that it was as fast as 3.2 gigahertz Intel chip. I'd say Intel was the one focusing on the speed (clock speed, that is).
You'd rather have superior technology than gaining a few microseconds? In case you didn't notice, as far as processors are concerned, they are the SAME thing. Superior technology (higher clock speed [all other things being equal], bigger caches / memories, smarter use of smaller and smaller transistors) literally translates into faster instruction execution.
THAT being said, back on topic. If you're a gamer / render 3d scenes then worry about performance. Otherwise, buy whatever mid to high range processor is on sale and you'll be fine. Typically AMD is considered to be cheaper and unless you're really taxing the processor, you won't notice a difference. Use the saved money to buy more RAM or a bigger / faster hard drive. Chances are you're not made of money.