Tomasi said something about Rebirth Superman being more thoughtful and not not being as impulsive as New 52 Superman, even though that's not how either Jurgens or Tomasi wrote Rebirth Superman early on, including the Lois and Clark mini.
New 52 Superman going for Mxy's throat appears to shock Jon a bit based on the expression he's making, while Rebirth Superman's aggressive behavior never appeared to shock Jon. Actually, while watching the confrontation between Superman and Luthor, he actually thought it was cool that the two of them were going to fight.
When he saw Superman attacking Eradicator, he wanted to join in.
There's also a contrast between Rebirth Superman and New 52 Superman in this crossover, even if it isn't that well done. Rebirth Superman grabs Fake Clark by the collar after Jon's disappearance, he realizes that Fake Clark had something to do with what happened to Jon, so he has a reason to be extremely angry the way he was at the apartment. Here, New 52 Superman is not really aware of what's going on, he's confused, and his response to grab Mxy by the throat and demand answers. He doesn't have a reason to be angry as Rebirth Superman was, but he is.