I don’t have either of these and I have not compared them side-by-side, so I hope someone who has will respond.

Bill Rupert has said that his favorite distortion is the Deluxe Big Muff Pi, and of all the Big Muffs it is the most flexible in terms of adjusting the tone and feel, that is how it responds to your picking, volume control, and other effects on the chain. In his demo video, Bill Rupert says that he can dial in the sound of just about ever other Big Muff ever made, but clearly there are some that are probably not possible because they are based on very different circuits – Germanium Big Muffs and OpAmp Big Muffs for instance.

The Green Russian, and the reissue, are based on the standard Big Muff circuit. The main thing that the Russian Big Muff was known for was its persistent low-end response. The Deluxe Big Muff Pi has a bass boost switch, a tone control, and a parametric mid frequency EQ. I would be surprised if you couldn’t dial in a sound that is VERY close to the Green Russian. Would it sound EXACTLY like the Green Russian? Maybe someone with really good ears could tell the difference in a blindfold test. But, I think you can get VERY close. In a mix I think it would be very difficult to tell the difference. Another thing to consider is that many early EHX boxes had lots of variation among themselves because of different sources for the components, etc. So, what EXACTLY does a Green Russian sound like? One might sound different from another. Of course, the reissues are more consistent because of better quality control.

In terms of feel, the Deluxe Big Muff also gives you control over the ATTACK and has a SUSTAIN control that covers the range of gain of probably every Big Muff ever made.