I expect the chess engine to be very similar between: Mirage, 1st and 2nd version of Ivan The Terrible, 1st version of Igor, Grandmaster.
Igor and Grandmaster have 1KB RAM, Ivan and Mirage have 2KB RAM, so maybe the latter 2 are a bit stronger? I don't know how the extra RAM is managed.

Igor versions, from Ron Nelson's notes.

1997,711E,Igor,Hitachi HD6433214P12 (H8/3214),5/5/1997,H8/3214 32-KByte ROM; 1-KByte RAM; 12 MHz,EWIG
2000,711E-2,Igor II,Samsung KS57C2308,10/4/2000,4-Bit core SAM47 KS57C2308 8K Bytes ROM 512 Nibble Ram 1.0MHz,EWIG

So yes, the 2nd version is weaker hardware.

There is no rerelease of Ivan The Terrible on a weaker CPU AFAIK. In fact, the 2nd H8 version of Ivan The Terrible may be even a bit stronger, since it's on a 12MHz H8 instead of 10MHz(20/2).