The case for the Los Angeles Lakers preferring P.J. Tucker:
P.J. Tucker is more experienced as a role player on a contender
Blake Griffin has never really been a role player in his career and that is what he is going to be on any team that he signs with this season. He is no longer the superstar that he was earlier in his career and we have never seen how he operates as the fifth, sixth or even seventh option on the team.
P.J. Tucker has made a living being that guy and has been a hugely impactful role player for the Houston Rockets. He knows exactly what it takes to be a role player on a title-contender and being a complementary piece, not the main piece.
It sounds trivial, but it makes it easier to implement him into the rotation in the short amount of time they would have to do so.
P.J. Tucker is a better defender
While the Los Angeles Lakers need offense more than defense, they still are a defensive-oriented team and the hope may simply be that the offense will come back when Anthony Davis comes back. If they value defense, Tucker is the better option.
Tucker has been pretty inefficient offensively this season for the Houston Rockets but I do think that would improve on an actual title contender. While he still was not great last season, he certainly held his own offensively.
He is much better defensively than Griffin, though. Tucker is far off from the best version of himself defensively but even on the Rockets, he is a league-average defender, playing in a large role. In a more confined role on a defensive-oriented team with help around him, Tucker could be even better on the defensive end.