They look to have the same ribbon motor and I'll bet they have the same, or similar transformer. So I bet the biggest difference between the two will be the MXL R40 comes with a shockmount. I have a Nady RSM-5, very similar to the RSM-4, and I love it for mandolin, drum OHs, and electric guitar. The mic clip it came with was worthless though, it's made of a soft rubber that won't hold the weight of the mic. I imagine the difference in the sizes and shape of the headbasket would make some subtle differences, and the MXL R40 looks like it's body my be more prone to resonance, as pointed out earlier, but I'll bet in 99% of situations, if one works well, the other one will too.
There are lots of threads that talk about how to improve the sound of these, by removing windscreens, dampening body resonance, retensioning and/or replacing the ribbon material, and transformer swaps. Any quiet pre with a good amount of gain will work with these. I'd look to something with a high or variable input impedance as well, as this will usually open up the high end. Preamps with a ton of quiet gain can get expensive so you may want to look at getting a FEThead or Cloudlifter to squeak out a bit more gain from your current setup and stay on a budget. Of course if you're only going to use the mic to record loud sources anyway, then that won't matter.