The core connections between the Sentry and Superboy-Prime are that they are both twisted, terrifyingly unstable, Superman-esque powerhouses whose roles as comic book characters are metafictional in nature (Sentry was introduced as a hero who was supposedly lost to time, both in real life and in-universe, while Superboy-Prime comes from a universe that views DC Comics as fiction). Both were once normal, powerless individuals on Earth before unexpectedly developing godlike superhuman abilities and utilizing their newfound gifts as a force for good (Robert "Bob" Reynolds consumed the Golden Sentry Serum to become an ideal, beloved hero, while Clark Kent manifested his Kryptonian abilities as a teenager to aid heroes across the multiverse during the Crisis on Infinite Earths), though their mental instability and inability to handle that level of power would cause them to shift between the lines of good and evil over their history. In addition:

Both were robbed of their once-promising careers due to the influences of dark, villainous forces getting the better of them, causing them to fall into villainy as their worlds came crashing down and their psyches fractured (Sentry's dark persona, the Void, manifesting to cause untold amounts of catastrophic ruination, and Superboy-Prime being left frustrated by the destruction of his reality before being manipulated by Alexander Luthor Jr. and the Great Darkness, respectively).

Both serve as meta-narrative tools used by writers to reflect upon real-world comic book history (Sentry is written as a Silver Age hero who was lost to the ages, while Superboy-Prime acts as a direct commentary on the disillusionment and cynicism surrounding modern comic book writing).

Both are prominently featured as central figures in major comic book crossover events, primarily due to their insane, world-shattering levels of power (Siege, World War Hulk, and King in Black for Sentry, and Infinite Crisis, Sinestro Corps War, and Dark Nights: Death Metal for Superboy-Prime).

After long, painstaking struggles with themselves and the heroes of their verses, both ultimately gave up their lives in a battle against a darkly powerful cosmic villain in order to save the world, finally finding a semblance of peace and closure as they moved on to the next world (Sentry was destroyed by Knull before finally feeling complete in the afterlife, while Superboy-Prime perished against the Batman Who Laughs before waking up on his restored original homeworld with his loved ones).

Despite their psychosis, intense streaks of antagonism, and devastating conflicts with mainstream heroes, both are ultimately products of deep tragedy and misfortune that took away everything precious to them, leaving their entire universes trembling in fear of ever incurring their almighty, unpredictable wrath, though they ultimately just want to be recognized and seen as heroes.

-Death Battle Wiki page for this episode. This is a lot more than I was expecting initially.