So, something interesting here that had me perplexed for a bit!
By looking at the first two screencaps, it looks like Gannicus and Crixus wear entirely different necklaces, as Gannicus’ has a noticeable design (looks to possibly be two Celtic dragons) and Crixus’ has two heads that look like they could be eagles (?) (Roman design). However, if you look at the third screencap, Gannicus’ necklace has the two eagle heads as well [also seen here] (they are attached to/holding the middle piece with the Celtic dragons) — so sometime after Crixus attained the necklace, he switched the middle piece into the ring (with some sort of design?) we can see in his screencap.
This makes sense, as the necklace becomes his own symbol of being the champion, and is personalized accordingly. It’s also possible the necklace has been passed down champion to champion, and the middle piece is replaced to fit the persona of each gladiator (like Gannicus’ being Celtic dragons and speaking to his heritage). Crixus is seen wearing the necklace all through B&S and Vengeance, ever since he received it from Gannicus.