About this image

Just a comparison shot between my 3 Bethesda Cris characters; top is Oblivion Cris, the middle image is New Vegas Cris and bottom is Skyrim Cris. Also sorry about lopping off the sides of the Oblivion and Skyrim images of Cris I didn't want a massive white space next to the NV image of Cris (this is because I use a different method of taking screenshots in Oblivion and Skyrim then I did in NV) but yeah that's about it for the intro-y thing.

Actually there's a few requirements for a Cris in a Bethesda game:
-Blue eyes
-have a proficiency with single handed swords (yes NV Cris has this proficiency despite using her pistol when she gets up close and personal) as well as in unarmed combat
-have a canine companion (usually in the form of a husky, Oblivion Cris has only recently gotten one)

as for where they're each different; their personalities, their professions, preferred weapons (they always have two kinds of weapon they prefer (and there can be some overlap)), their failings/vices/weaknesses and their combat style are all completely different for example NV Cris is an alcoholic pyromaniac of an ex-mercenary whose preferred weapons are the sniper rifle and pistols (not revolvers though) and her approach to combat is to get the highest caliber rifle possible and shoot your legs out from under her opponent and leave them to bleed to death, whereas Oblivion Cris will charge you using a sword the size of a child, her other preferred weapon is a bow which she never uses she's a somewhat abrasive individual with no respect for authority despite being in the Chorrol (And later Kvatch) guard and is usually described as a cheeky rebel her main failing is a case of attention deficit disorder (ADD) which means she's easily distracted by shiny objects she also has a habit of misinterpreting things and taking the law into her own hands (with spectacular and mafia like results.)

As for the newest Cris, she's a thief (kinda inspired by jim_uk's character angel here, although Cris is actually competent) with a preference for daggers (she either dual wields two of them or uses one in her off hand (she's ambidextrous but was predominantly right handed before teaching herself to be ambidextrous) with her sword. Her other preferred weapon is also the bow which she uses more than Oblivion Cris and since she's Dragonborn she has access to shouts (her favourite one is the Fire Breath shout) her personality is also completely different from the other two Crises being mostly quiet and respectful (Although she can get very sarcastic) she doesn't have any failings/vices or weaknesses yet (unless you count her unwillingness to kill unless it's in self defense since she's a thief not a murderer) but she's a new character so that's excusable (in my opinion) again she's not a relation to Oblivion Cris, Oblivion Cris would be long dead by the time Skyrim rolls around.