Personally I like the spelling Vivian best. With that spelling it's one of my favorite names. I love the nn Viv. My main associations would be Aunt Vivian from the tv show Pushing Daisies and this snobby girl I knew with the name (and it shows how much I like the name that that association hasn't ruined it for me).
From those I like Vivien better, but I like Vivian most of all. It feels the most down-to-earth of the three imo. I think it's vintage & soft, but stronger than a lot of popular vintagey type names. I think it reminds me of Lydia in vibe. Girly/vintage, but tougher than the Em- Elle- & Ad- names & all of the flower names.
I love it. Totally nms either, but I kind of dig the girly French flair of Vivienne. Vivien/Vivian are fine, but my brain somehow reads those two as anagrams of Evian (I think it's some kind of strange dyslexic thing particular to this name).
I don't have any personal association with the name. Vivi would be a cute nn.