I do think the custom characters do struggle when you compare them to their origin counterparts, even in BG III.
Take Lae'zel for instance. Play a Githyanki fighter and try saying with a straight face that you feel like you have an equal but distinct experience from Laezel. You can't. Particularly with her in the party, you see tons of reactivity from npcs that you don't see as a custom githyanki-even though your backstory is essentially the same.
You drow ranger has the benefit of
A) Being a member of the race with the *most* extra lines written for them, and B) There are no drow origin party members, and no ranger origin characters (till minsc arrives, at least)
A somewhat common observation during EA has been that drow characters have the most unique experience, so this is a very special case.
Similarly, we can look at Shadowheart & Wyll. Shadowheart is a cleric, and Wyll is a warlock, players can choose to also be a cleric or warlock, but they will not have the unique relationship with their faith that she does in the story, even if they also choose to be a cleric of Shar or Selune. (it's actually kinda eyebrow raising how little anyone cares about you being a cleric of Shar or one of the other evil deities, IMO) Likeswise, non-origin warlocks don't get to interact with their patron at all, while Wyll has this big plot interwoven with the main storyline looking for Mizora.
