Let's summarize every processor's pros and cons:
Look at individual processors.
Note: Usually Cyrix processors carry the designation IBM. IBM just manufactures them, Cyrix designs them; Cyrix is a fab-less chip vendor.
 

I' Bandwidth and performance flaw
 
'normal' with the flaw:  (best in red, second best in blue).

rates Mb/sec	Pentium MMX-200	AMD K6-200	Cyrix 6x86MX-166 (P200)	Pentium II-233
Main memory read	119.04	118.34	118.34	183.48
L2 cache read	227.27	240.96	270.27	425.53
Main memory write	85.47	69.44	75.75	68.72
L2 cache write	85.10	128.20	157.48	210.52
Video memory write	79.05	51.02	81.96	25.47
Main memory transfer	49.50	38.53	38.91	48.19
L2 cache transfer	70.42	84.03	95.69	162.60
Video memory transfer	57.63	36.36	56.33	25.47

 
Conclusion:
Its easily visible from the above table that bandwidth-wise the Pentium II is the best and also that the best of the socket 7 trio is Cyrix 6x86MX. Note: On Pentium II the use of a small utility (e.g. FASTVID) will increase significantly the video write and transfer rates (they will exceed Pentium MMX's).
The reason why Pentium II has such improved rates is that on main memory it supports multiple outstanding bus transactions and that its secondary cache is on board, operating at 233/2=116.6 MHz instead of the 66 MHz of socket 7 processors.
 

'innovative' without the flaw:  (best in red, second best in blue). 
(The innovative write rates on the table are achieved using 64 bit writes, a method documented by Intel in its 1997 Optimizations manual; the 'performance flaw' revealed in this site affects the read & transfer rates).

rates Mb/sec	Pentium MMX-200	AMD K6-200	Cyrix 6x86MX-166 (PR200)	Pentium II-233
Main memory read	200.00	119.76	200.00	191.64
L2 cache read	344.82	256.41	294.11	512.82
Main memory write	170.94	68.96	75.18	69.54
L2 cache write	170.94	116.95	170.94	210.52
Video memory write	92.59	92.59	92.59	51.02
Main memory transfer	95.23	40.24	43.85	50.28
L2 cache transfer	119.04	82.98	94.78	165.28
Video memory transfer	68.45	56.33	64.51	41.75

 
Conclusion:
With the workaround applied, it is easily visible that bandwidth-wise Intel's processors are the best; the difficult thing is to choose between Pentium MMX and Pentium II; with FASTVID applied, Pentium II has the edge. (But don't forget: Pentium II runs at 233 MHz, while Pentium MMX at 200. A 200 MHz Pentium II would be outperformed by Pentium MMX).
The reason why AMD K6 has almost the same values as in the 'normal' table (except video read/transfer) is that the flaw is not correctable on K6. (Though it is correctable on the K5).
 

II' DOS benchmark

(best in red, second best in blue)

CBENCHP	Pentium MMX-200	AMD K6-200	Cyrix 6x86MX-166 (PR200)	Pentium II-233
loop (µSecs)	0.54	0.63	0.37	0.44
64k program (µSecs)	0.58	0.53	0.45	0.53
transfer rate (Mb/sec)	62890	74350	79680	157480
video write (Mb/sec)	81300	51020	81970	25470
Index relative to IBM PC	291.5	284	373	340

 
Conclusion:
In DOS or 16 bit programs Cyrix 6x86MX PR200 is the best with second Pentium II-233. Note: On Pentium II the use of a small utility (e.g. FASTVID) will increase significantly the video write, to 85840, but the final index will still be lower than Cyrix's.
 

III' Windows 95 benchmark

On Windows 95, Pentium II-233 is clearly the best, with second Cyrix 6x86MX.
But its important to note, that a K6-233 reaches 55.3 and a 6x86MX PR233 (188 MHz) reaches 56.6 !
 

IV' 3D/Floating Point benchmark

On Quake, Pentium II vastly outperforms all the other processors, while second comes Pentium MMX. The reason for that is that Pentium II has a next generation floating point unit which is almost twice as fast. Pentium MMX outperforms the last two because AMD and Cyrix have simpler and slow floating point units.
 
 

Final conclusion

From the above it is obvious that the best processor in everything except 16 bit (DOS) is Pentium II; of course Pentium II is also much more expensive and needs a special expensive motherboard (slot 1) on which only Pentium II can operate.
For users with a recent motherboard who wish to upgrade, the best solution is to upgrade their processor to a Cyrix 6x86MX if they are interested in general performance or to a Pentium MMX if they are interested mainly in 3D game or calculation performance. The middle way, some general performance and some 3D, is AMD K6.
Cyrix 6x86MX: The good news for budget users is that the cheapest by far processor is also very good in general performance, as long as they can compromise on 3D/calculations. Especially the PR233 version (188 MHz) almost catches up with Pentium II-233 on Windows 95.
Finally for professional Windows NT/CAD/3D/calculation users there is no serious alternative than Pentium II at the moment. The same applies to avid gamers, especially due to Pentium II's new AGP graphic cards.

For questions, go to the Q&A page.
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