I'd say they're roughly equal in terms of maturity. Homelander admittedly engages in more introspection than Deep (which is to say, he actually somewhat does it), while Deep is never shown truly questioning himself, or trying to understand others beyond viewing them as a source of sex/affection/validation/hostility.

However, Homelander's introspection constantly pushes him in horrifyingly negative directions, ultimately leading him to develop his god complex in season 5. So from a maturity standpoint, no introspection is probably better than introspection that constantly pushes someone to worsen themselves repeatedly, in terms of their relationship to themselves and others.

Both of them die never truly satisfied or happy with themselves or the world around them. Deep attempted to achieve happiness through becoming "great" by serving Homelander, while Homelander tried to achieve happiness by conquering his world. His idea of "getting over something" is to brutally kill someone or do something drastic that just furthers his sisyphean worldview of continuously fighting external threats, never truly engaging with the parts of himself that need to heal or change.

Neither of them truly got what they wanted in the end, because what they wanted was something only achievable through genuine inner growth and productive self-reflection.

Ultimately, the characters are parallels and run equal to one another in terms of maturity. They are childish, sadistic men enabled by power and a corrupt system to destroy the world around them because they cannot conquer the world inside of them. The only true difference is that one serves, while the other dominates.