Although I'll be ABLE to play any race in any faction, except for my one Imperial I'm going to stick to the "native" races for each faction since at least some of the dialog/interactions will be tailored for those races.
Cases in point:
In EP, you can ask a Dunmer about the races that make up the Pact and she'll give you her opinion of the Argonians, Nords and Dunmer with the things she says subtly influenced by YOUR race. If you are an Argonian, for example, she'll point out that Dunmer used to enslave Argonians and she'll add, "Sorry about that" or something mildly amusing. If you are a Nord and ask her about the Nords, she makes some dry witty comment about "it's just like a Nord to ask that kind of thing" or something (mildly insulting the intelligence of the race). And if you're a Dunmer she'll say something like, "I don't know about YOU, but---" since she recognizes that you are Dunmer, so she offers ~her~ specific opinion of her own (and your) race.
In AD, there is a Bosmer/Khajiit "re-education" school. I only ever visited briefly with my Altmer, but I'm quite curious to see the dialog my Bosmer or Khajiit would face when talking to those "instructors" who were telling Bosmer to renounce the Green Pact (daily!).
Playing some other race, I'm not sure WHAT the dialog would look like --- how would a Dunmer talk to an Altmer? How would a Khajiit talk to a Nord?