I’m not saying that it’s only a loudness thing, but the snare and other elements are definitely louder in the Logic render. It’s not simply a matter of them sounding clearer or more detailed somehow; they are absolutely louder to start with, no question. For whatever reason, those elements are louder in Logic than they are in Cubase. It could be a slightly different setting for send tracks, or a different gain curve, or who knows what. Whatever it is, you probably need to compensate for this difference in gain before a proper test can be done.
If you’re processing those particular elements (snare, vocal, guitar, etc) through additional effects, then the fact that these elements are louder (for whatever reason) can easily have a knock-on effect through the DSP chain. A louder input signal means that more of the frequencies are being sent through any filters, eqs, reverbs, distortions, or anything else you have on there. This louder input could easily produce a final processed sound that has more exaggerated/boosted frequencies in Logic, and this could manifest itself as sounding more crisp or clear or whatever.
I don’t have Cubase or Logic here myself to really test this with, so I can only base my assumptions on the files that you have provided. But I can tell you this for sure: the kick and bass in both renders are essentially identical. They have the same gain level, same frequency response, etc. There is no appreciable difference.
The easiest way to prove this is by inverting one of the renders and then mix-pasting it back onto the other render. Whatever remains after this process is the difference between the two signals. The idea is that two perfectly identical signals will ideally cancel out to complete silence, whereas two slightly different signals will result in some subtle residual noise, and two very different signals will result in much more dramatic residual sounds.
When I apply this process to the two renders that you have provided, I get the following result:
vacdecubaselogicdifference.wav
You can listen to it yourself and see that the kick and bass sounds have obviously disappeared completely, leaving only the snare and other elements remaining. This is pretty conclusively evidence that the kick and bass sounds in each render are basically identical. Whatever differences you were hearing with the kick and bass must be related to the live playback in each DAW, since those differences are not actually showing up in the final rendered output.
If the Cubase rendered kick and bass sounds were physically more full, or had more bass, or were different in any other way, then this would be immediately obviously after the mix-paste process. There would be a pretty obvious amount of residual sound left over from the process, just like there is some residual sound from the snare and other elemtns that were different in each render.