These are the real, original bronze ones, stolen from Constantinople by the Venetians when they conquered the city in 1204. They were probably taken from the Hippodrome in Constantinople (there's some doubt, though, as to where they had been placed). The Venetians put them up on their Basilica. Napoleon stole them again, but after Napoleon's downfall the Venetians (not the Constantinopolitans) recovered them. But they were suffering from the elements in their perch on the Basilica, and now they are kept inside the Basilica museum.
Just a few paces away from the originals are these copies, placed where the Venetians displayed them in the days of their vast commercial empire. (Ignore the guy in dark glasses who looks like he's about to be clobbered by a hoof.)