Those comparisons included scoring leader Carlos Vela.
As usual, the forward backed up his words on the field.
In a matchup between the league's top two scorers, Ibrahimovic scored his second hat trick in MLS and led the Galaxy to a 3-2 victory in the first meeting between the two clubs this season.
"I have a lot of respect for Vela, he is a good player but you did one mistake, you compare him to me. That was your biggest mistake," Ibrahimovic said after the game.
Ibrahimovic — who is second in the league with 16 goals — scored in the eighth, 56th and 70th minutes. His first MLS hat trick came last season against Orlando City.
The 37-year-old Swedish star has played his best against in the rivalry nicknamed "El Trafico". He scored two goals last year in his Galaxy debut last March, which was also the first-ever meeting against LAFC, and has six goals in four matches against Bob Bradley's team.
Vela scored twice for LAFC, which lost for just the third time in 21 matches this season. The forward has 21 goals in 20 games and is the fastest to reach 20 goals in a season in MLS history.
LAFC (14-3-4) leads MLS with 46 points and has been a juggernaut since joining MLS last season. But the one thing it has not been able to do is defeat its rival 12 miles to the south. The Galaxy have a 2-0-2 edge in El Trafico.
"You play against certain teams and there is a guy that is a strong personality," Bradley said. "We have to take our football and make it so strong that at the end of the day we don't deal with all sorts of questions about him."
Besides temporary bragging rights — the two teams meet again on Aug. 25 — the Galaxy (12-8-1) moved into second place in the Western Conference with 37 points — have two wins while the other two ended in ties.
LAFC opened the scoring in the fourth minute when Vela converted on a penalty kick. Vela drew the penalty when Galaxy goalkeeper David Bingham came off his line and upended the forward near the goal.
Ibrahimovic evened it four minutes later when he got the feed from Julian Araujo, split defenders Walker Zimmerman and Eddie Segura and fired a shot from the top of the box that beat LAFC goalie Tyler Miller.
Ibrahimovic then gave the Galaxy the lead 11 minutes into the second half when he took a crossing pass from Diego Polenta, went over Jordan Harvey and headed it into the net.
He completed the hat trick 14 minutes later with a blast from 21 yards out off Favio Álvarez's pass.
"I always come in with a lot of confidence and belief. When I go out on the field I feel the responsibility," Irbrahimovic said. "The outcome was perfect."
Vela brought LAFC within a goal in the 97th minute off Eduard Atuesta's assist.