It's similar to the first one, a lot of call backs to the first Gladiator and there is the obvious tie in as well. Obviously loosely based on anything historically factal, there were Gladiators and they fought and died brutally and Rome was in a state of massive corruption during this time as well. So your extremely high-level view of the historical facts, there were twin brother Emporers and Gladiators who fought and died brutally in the Colosseum and Rome was at the beginning of its end during this period of time, but beyond that that's where the historical facts start and end.
As for historical facts about the Colosseum, the Gladiator games lasted for 400 years, which is crazy to think of. And in that 400 year span, it is believed that 400,000 to 500,000 people were killed in these games. That's over 1,000 people a year died in this arena for sport and entertainment. Millions of animals were also killed.
The last Gladiator fight to take place in the Colosseum was attempted to be stopped by a munk, who jumped down to the floor and got between the fighters to try and stop them from killing each other, and the crowd ended up stoning the Munk to death for it. The Emporer at that time then put an end to the Gladiator games, that was in 404 AD. However, they would still hold Person vs Animal hunts or fights for another 100 years.
Pretty good movie, it's in my opinion worth seeing in the theater. I really love the history of this time period.