Yes, there are definitely parallels. But I wouldn’t call Asami the equivalent on Suki. Suki got a way better deal in A:TLA than Asami did in LOK.
Never pitted against another woman in terms of romance (in fact she was super nice to Toph and they had some great scenes together). Her main emphasis in the story did not come from who was bangin’ her. She actually got to have real female friendship in the show. Oh, and Sokka was super nice to her. Asami in her parallel narrative arc got virtually none of these things. So yes, while they are some aesthetic similarities, in terms of writing Suki did way better.