After initially encountering one another as adults and members of the respective world's greatest superhero teams, the Supermen were time and again drawn together when crisis after crisis threatened both planets. This was during a period when the aged Man of Steel resumed his career from which he had briefly retired, which was still early in the career of the younger Man of Might. Nevertheless, each displayed similar levels of courage, determination, and conviction towards protecting their respective Metropolis.
When Creator2 sent his eerie employees to defeat the Justice Society of America, allowing for his plans of destroying Earth-Two for a cosmic construction project to proceed unchallenged, Superman was first to face the alien adversaries. When a snare-web weakened the Man of Tomorrow, his counterpart was equally effected with both immobilized in a weakened state for the remainder of the tyrannical threat to both worlds. It fell to their comrades to determine the source of the parallel plagues to the powerful protectors, with the JSA defeating the malevolent mastermind and his menacing minions.
During the subsequent crisis a year later, when aliens A-Rym and his pet Teppy were separated during an interdimensional voyage with their family, it fell upon the Supermen and their allies in the Justice League and Society to deal with both. However, neither seemed to measure up to Teppy physically although they outwitted it by isolating it on a man-made plateau.
During this same case, Earth-One's Superman journeyed back to Earth-Two to face off against Solomon Grundy and was soundly defeated until joined by his allies. His counterpart would eventually himself battle Grundy alongside cousin Power Girl, wherein the pair would deposit the man-beast in a volano. Back to this case, there was very little one-on-one interaction between the Kryptonians, perhaps due to some strained relations from their previous meeting in the presence (and manipulation) of Aquarius.
However, another crisis would draw this potent pair together, literally, and would bond them in a way unprecedented and never to be repeated among connterparts...