From his bits of dialogue in the Japanese games
>Uses boku as his personal pronoun, common for boys. In comparison, the rival uses ore, which is typically used by men or boys trying to show off, it matches his high opinion of himself, and he even starts arrogantly referring to himself as ore-sama (-sama is a respectful suffix attached to people of much higher social status, like lord/master)
>Uses standard dictionary Japanese one would expect a boy to use, not the more polite speak (desu/masu) often used by girls or polite boys
>Will use shortenings like -(a)nakya instead of -(a)nakereba, asks questions with an -i sound at the end which is a bit more a familiar with someone way of speaking
But he also says the in-battle lines when switching out Pokémon. An NPC on the S.S. Anne comments that the player doesn't talk much though. And like many boys, he likes video games because he has a Famicom in his room.
In comparison, Brendan's dialogue (as a rival and in Masters where he's the Hoenn protagonist) is much more hotblooded shounen in nature. It's a bit cockier and less respectful, though not to the same degree as the Gen I rival is. But while Red has an interest in video games and movies, he also has a drive to become a Trainer and aim for the top that draws him away from home, and he continues to be devoted to that to the point he doesn't come home for 3 years and does solitary training on top of a mountain as the strongest Trainer.
When it comes to what other characters think of him, his rival sees him as weak until he gets humbled as the Champion, but also recognizes him as his best friend and a goal to overcome. Other characters see him as a legend, the only outright acknowledgement of "I did all the stuff in my debut game" while other protagonists don't appear as NPCs in later games, so they don't have histories.
Overall, Red is the typical blank slate Trainer. Competitive, aiming for greater heights, eye contact, to the point that words are unnecessary.
