Should probably try to answer the original question…
If I recall correctly @reeve_mike has ATC loudspeakers in his Rossini system and he may be able to offer some insight into what has and hasn’t worked for him.
All things being equal it doesn’t really matter which output you use. Both are excellent. The choice comes down to the downstream components and their designs / implementations. If the downstream components are truly balanced (and not all components with XLR connectors are) then the balanced output on the Bartók is preferred.
In your case I’d recommend the balanced outputs as they will provide the best interface with the electronics in your speakers and also give you the most flexibility in placement of the Bartók within the room.