Red becomes Kanto champion around the same time as Brendan.
Both games are compatible and allow to battle each other. Red wins it.
Lucas after accomplishing the events of Arceus gets send back to the present.
Ethan becomes champion around the same time as Lucas and battle off same as with RSE and FRLG both games are compatible for battle.
Event Arceus for DPPt which unlocks the HGSS event can only be obtained by trading from DPPt. Arceus however doesn't just acknowledge any trainer.
Ethan won the battle against Lucas and has gotten Arceus approval. Lucas than trades Arceus to him. CANON
Now at Mt Silver the battle of Japan region champ is at stake.
RED VS ETHAN

Of course... the prodigy wins. None other than... RED. The living Legend.
How do we know this? very simple Red keeps appearing in future installments while the rest are obsolete. Red also participates in the PWT and wins. Opens up his own Battle fatcory in Alola and has the title of living legend.

RED IS HIM.

UNDEFEATED UNDISPUTED POKEMON WORLD CHAMPION.
RED THE GOD THE MYTH THE LEGEND HE IS HIM.
CANON