Questions and postings pertaining to the usage of ImageMagick regardless of the interface. This includes the command-line utilities, as well as the C and C++ APIs. Usage questions are like "How do I use ImageMagick to create drop shadows?".
IM delegates the rasterizing of SVG to one of three delegates: MVG, RSVG or Inkscape. I suspect your two computers use different delegates, or different versions of the same delegate.
"-verbose" in your commands may explain. You could paste the text output here.
If your delegate is Inkscape but an old version, I suggest you upgrade.
MVG and RSVG can rasterize SVG, keeping transparent backgrounds, by using "-background None" as you have done. Perhaps you need to upgrade IM to get this. Or perhaps the SVG contains something that prevents MVG and RSVG from doing this.
Perhaps you are using the internal ImageMagick MSVG/XML renderer, which on older versions of ImageMagick is not as good as Inkscape or RSVG. If so and you do not want Inkscape, then install the most current RSVG delegate into ImageMagick on both systems. You can check if you have it as a delegate using