Wow, no love for the Cyrix here. :D
I upgraded from a Pentium-75 to a 6x86L in 1996 or so, and bought a 6x86MX in 1999, which I used until I could upgrade to a K6-2. The Cyrix chips were great for running integer-heavy apps, and much more cost-effective than anything else available at the time. I may have only paid $40 for the 6x86MX--it was a very, very inexpensive chip. At my first job, when times were tough and we had a lot of people forced to run Windows 95 and Office 97 on 50 MHz 486s, I built a lot of Cyrix-based systems on the cheap to help those poor souls out, to get them something that would run Win95 and Office 97 effectively. I'd pick up an Asus motherboard and whatever Cyrix CPU we could afford, along with the cheapest PCI video card I could find, then recycle the 72-pin memory and hard drive from their 486. It wasn't optimal, but it let people spend a lot less time staring at an hourglass.
But once mainstream CPUs hit 350-400 MHz or so, Cyrix couldn't manage to keep up. I'm not sure what the problem was. AMD and Intel pulled away, and I upgraded the 6x86MX to a K6-2, and bought a Slot 1 Celeron-based system to learn Linux on. The Mendocino-architecture Celerons were a very good value for the money at the time.
I hung in there with Cyrix as long as I could, and was sorry to see them fade away. Cyrix seemed to plateau before Natsemi bought them, and Natsemi didn't do anything to break the slump. VIA bought both Cyrix and the Winchip from IDT, merged the teams, but the "VIA Cyrix" branded chips were actually a Winchip design.
I used a few Winchips in my day too, because they were direct replacements for pre-MMX Pentiums. I think I could put them in systems that topped out at 133 MHz, set the multiplier to 1.5, which it used for a 3.5 or 4.0 multiplier, and get something higher than 200 MHz. They were like a Pentium Overdrive chip, but they cost half what the Intel chips would have, and they were fabulous for running productivity apps. They weren't good for games, but since we were using them in an office environment, we considered that a feature.
The integer performance of a Winchip was pretty close, clock-for-clock, with an Intel Pentium, as I recall.