Think of series like the Elder Scrolls, Dragon Age, World of Warcraft, Dungeons & Dragons, Pillars of Eternity, etc. Which of those games had the best selection of character races to choose from?
Which game franchise handled characters races the best?
Probably Starcraft
Not really a race (and not really a franchise), but the factions of Alpha Centauri are really well thought out in my opinion
None of them handled them greatly, but Elder Scrolls from what I have seen. They weren't afraid to be extremely racist.
I'm not really familiar with the other games except for Elder Scrolls. In my opinion, I think they handled each race pretty well and even added in some dialogue to each specific race you choose. Ex. in Skyrim, if you are an Argonian, some will comment how you originated from the Black Marsh. Also, I believe there are villages that only have Orcs in them. There you can learn a little about their culture.
In Morrowind the Dark Elves were very racist against the other species. There was a wizard that you talked to during the game who would say things like Khajits are only good as slaves and stuff. In Daggerfall, there was also people you could talk to that would say incredibly racist things. They have dialed that aspect back in the last two games.