Pentium MMX is pretty much exactly what the name implies: a standard in-order Pentium CPU, with MMX instructions added.
However, because of the extra instructions, the decoding pipeline had to be modified somewhat, which makes certain operations 1 cycle slower than they were on a Pentium classic.
On the other hand, the Pentium II has a very different architecture, with deep pipelines and out-of-order architecture, which can reorder instructions at runtime (technically a Pentium II is what you'd expect a 'Pentium Pro MMX' to be). This new architecture has higher latency when executing instructions, but also has advanced means to hide this latency in many cases.
What it boils down to is that at the same clockspeed, the Pentium MMX can sometimes be faster than a Pentium II, especially with MMX code, when the Pentium II is not able to hide the latency well enough.
But the Pentium II compensates for that by offering much higher clockspeeds (the fastest Pentium MMX is 233 MHz, which is equal to the slowest Pentium II).
Aside from the CPU itself having higher clockspeed, the PII also came with new chipsets with higher FSB speed, AGP bus and support for faster memory.
For non-Intel CPUs like the AMD K6 series, a 'super socket 7' platform was developed, trying to backport these new technologies to socket 7-based CPUs. So you can get faster FSBs, AGP and faster memory on these socket 7 boards as well.
But afaik a Pentium MMX cannot take advantage of any of this.
To me, the Pentium 233 MMX is just the 'ultimate Pentium'. The last in-order x86 from Intel. So as far as Pentiums go, it's the best you can get.
But it won't stand up to the Pentium II or clones like the K6-series which can take advantage of super socket 7.