Here's the three examples I use for my issues with performance of AMD/ATI:
In 2000 I was moving across country. I had an Intel 266Mhz at the time. I pulled out my video card and RAM and took it to my mom's house. My plan was to build her a new computer and use my RAM and video card temporarily so I could play everquest. I ended up buying an AMD 450Mhz CPU. I installed Windows and EQ. But.. the game was choppy and unplayable. Note that I was using the exact same physical RAM and video card, but despite AMD's clear advantage of almost 40% it STILL couldn't cut it.
In 2003 I built a Windows Server 2003 machine. At the time nvidia said no drivers would ever be released for server 2003. So I went to the store and bought an ATI video card. I spent $250 on the card. I only intended to play games that were at least 2 years old so I knew I'd still be fine for performance. I got home, installed my video card, and started installing games. Every single game I tried to play was not compatible with my video card without some custom patch from the game manufacturer. I had 5 games and had to install 5 patches manually to get each to work. Halflife didn't work for squat even after the patch. The menus were unreadable and I couldn't even play the game. A few phone calls and.. sure enough, if you happened to have my video card you were screwed. The video card had some hardware issues that ATI didn't fix.
In 2006 I bought an AMD laptop. They were significantly cheaper than the Intel based laptops. All I wanted to do was be able to take some 720p videos with me and play them during my travels. The laptop could perform fine, until it was unplugged. The second it was unplugged the CPU artificially lowered it CPU speed by 2 or 3 multipliers and movies wouldn't play. I took it back to the store and they couldn't fix it. I called the manufacturer, and they told me it was "by design" this way to prolong battery life. I went looking all over for power management settings so I could set them to maximum performance, but it didn't matter. I went into the AMD forums and everyone complained about the same thing. I asked friends that were avid AMD users and they couldn't help me. Ultimately I ended up returning the laptop and had to eat $150 restocking fee.
So while AMDs may have a purpose for many people, they seem to fail, horribly, every time I try to use them.
Let's not talk about instability issues I've had that were later determined to be problems.. IF you had an AMD CPU. I have a screenshot from years ago in EQ where it had a message at the login screen that if you owned an AMD CPU you couldn't play and that a patch was forthcoming. I LOVE rubbing that in my friend's face that swear by AMD just because I can
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So while friends swear by AMD and/or ATI, I've yet to ever be happy with the performance of an AMD or ATI product. I've lost so much money over the years it's cheaper to "cut my losses" and buy Intel despite the higher price.