I was switching from ArcGIS to QGIS years before. Since I’m working with LGIS (2014 or so) I’m usually not taking Shapes but prefer to involve LGIS project.db (which now can be named individually - pretty thing!) directly to QGIS. This is running perfectly without any projection issues. If really necessary I’m exporting Shapes from QGIS. But I have no more experiences how ArcGIS handles such stuff.
When in rare cases exporting Shapes from LGIS I know how my layers are projected - this is continued in exported Shapes. So you may only choose same EPSG as in your LGIS project.
By the way an idea for further development: could be helpful to have a general setting option for ‘standard projection’ (which is usually WGS84, but I in general prefer EPSG:25833) as well as standard coding (which is usually UTF8). Is there a chance to implement such standard setting?