Brad Pitt is doing a subtly different performance in these two roles, using similar physical mannerisms, but not identical. A comparison can be drawn. Maybe Louis would be the colder version, Mills the hotter version, of reacting to this similar situation.

• Both have been roughed up somewhat by their antagonists at this point, but are dressed nicely. 
• Both are reacting to the first moment of being informed that their wife/S.O. and infant child was murdered (for Louis, Madeleine is the freshly made child!).
• What’s especially upsetting about Louis’s loss is that it echoes the beginning of the movie, in which he’d lost his wife and child in childbirth. He’s come all this way and IT F*&KING HAPPENED AGAIN GDI SANTIAGO ;A;
• What’s especially upsetting about Det. Mills loss is that he didn’t know he was going to be a father! ;A;
• Both have to grieve very quickly in order to move on to…
• ☆*:.｡. ~VENGEANCE~ .｡.:*☆
• Det. Mills serves it up fresh, impulsively, just walks right into the trap laid for him by his antagonist.
• Louis serves it a bit cooler, the next night, with some planning involved, and alot more death, taking his antagonists by surprise.
• Both essential use fire to do it. Firearm! Get it?? yeah.
• Louis knows Revenge is a dish best served en Flambé.