They certainly would. Shaquille O'Neal would explode for 35 point outings while fouling out DeMarcus Cousins and Kevon Looney. There is just no answer for him. How would the Warriors come with their doubles? Shaq was a willing passer though and the Lakers field a lot of clutch shooters.
A young Kobe would torch Thompson's (admittedly plus) defense and has the legs to chase him through a maze of screens. Thompson's handle is sub-par and if he tried to take Kobe man to man he would be mostly stifled.
Stephen Curry runs rings around Fisher but his anticipation would enable him to draw a charge and play good position. Fisher's clutch spot shooting was legendary.
In the clutch, Kobe has the lateral movement to match up with Curry and give him big problems.
Durant is an all time great point maker but Fox was a legitimate stopper. It is unlikely KD would dominate this matchup.
Horace Grant might not play much because his post up defense would be mostly useless. He was still a good rebounder. Edge to Draymond Green here.
The triangle would slow the pace and allow the Lakers to control the action. The Lakers are much slower than Golden State but because of Shaq's dominating presence it likely wouldn't matter.
Lakers win in six games.
The Spurs would present Tim Duncan as an unanswerable problem. His low post maneuverings were varied and explosive circa 2003. His mid-range jumpers were good enough to lure defenders closely. Had the poise to scan the floor when being doubled and deliver. He was the best defensive rotator in all of creation and a dominating rebounder. Does Golden State double on his first dribble or try to seal him baseline? TD would thoroughly dominate the action.
In the plus column for Golden State, Stephen Curry would abuse a young Tony Parker.
Klay Thompson would outscore Stephen Jackson and would easily discombobulate SJ's inferior handle.
The problem for Golden State would be Bruce Bowen. He was a powerful sticky defender who Kevin Durant wouldn't be able to go wild against. KD notoriously struggles (relatively speaking of course) against strong yet quick-footed defenders. And when the Warriors are scrambling their inside out rotations after responding to Duncan there would be Bowen to hit three point balls.
When paired with Duncan, Malik Rose at power forward was a highly underrated player. He would bang with Draymond Green, stick mid-range jumpers, and pound both boards. Draymond Green doesn't have as big of an edge as you think here.
Off the bench, Manu Ginobli was young and very mistake prone but capable of injecting juice into a ballgame.
The Spurs discipline would allow them to control the pace of play. They play better more consistent defense than Golden State is capable of. Duncan and Rose would play volleyball on the boards.
Spurs win a seven game series in six.