Did somebody say "Cyrix" (again!)?
There is one document which will answer all your questions concerning the performance of a Cyrix MII-366GP. It is the Ultimate 686 Benchmark Comparison. Refer to the link in my signature. Is your MII-366GP one of the rarer 2.2V pieces, or the older/hotter 2.9V chip? If it is the 2.2V chip, you can probably run it at 285 or 300 MHz.
If you want to run the chip at its stock rated speed of 2.5 x 100, or 250 MHz, then the OVERALL performance was about that of a PII-233. For a machine which mainly browses the internet or runs office-type appes, then it was about a PII-266. For gaming, it was only about as good as the original Pentium MMX 200 (as confirmed by Quake I and II benchmarks).
In reality, the max. stable speed you might be able to get out of any Cyrix MII is 333 MHz, which makes it about as fast as a PII-233 and AMD K6-2-400 in Quake II.
Plan your life wisely, you'll be dead before you know it.