In general it is not a good idea to share application from one Linux flavor to the other.
Even if both flavors were base on Ubuntu we can not rely on all shared libraries being installed, or have the version needed for a given application. It may work fine but in case there are issues we are faced with a confusing and hard to debug situation.
In addition, most applications heavily depend on libraries that had already been installed by the distribution. The benefit from sharing application binaries would be rather minimal.
Only rarely a self contained application binary compiled for the same architecture may successfully be shared (this may e.g. be the case for proprietary software or some games).
Even sharing application's settings from our HOME may cause trouble if the distributions came with different application versions that may have a differing settings format.
The Virtual Box application should not be shared between distributions, as it depends on at least one kernel module loaded at boot. But of course you can easily share the virtual machines without issue, provided they are accesible from and registered in the corresponding Virtual Box installation.