ubuntu-budgie-desktop is called a meta package. It is basically a package that installs all the dependencies and recommendations that make up Ubuntu Budgie.
Many packages are the same as Ubuntu’s meta package ubuntu-desktop. Not all the same though.
So by installing both you have the sum of both … more than just Ubuntu Budgie by itself.
Some of the packages use the same settings.
We also both update those app settings to reflect the defaults our respective communities want. Then the settings may not be the same.
This is where the conflicts are … by installing both you will get a different feel than if you just installed the one distro.
e.g. touch pad defaults, theming, default file manager, keyboard bindings etc.
At the end of the day all packages are from the same archive… so updates come to both distros… same kernel, same graphics drivers etc.