You should be able to prevent the horizontal/vertical overlapping of routed connections . This way the connections should be easier to differentiate.
To better differentiate connections, users might:
--- use labels on the connections
--- use bezier connections
--- use different colors for different connections
--- use more custom connectors and attach the connections to not used connectors
-- use AStartRouter instead of the default one (Grid Router)
This feature is available with our latest official version - R1 2019.