According to the books neither of the designs is "incorrect" because there is no description in the book so specific and detailed that it will be possible to determine which of these rings is more accurate. One description of <PERSON> can be found in The Fellowship of the Ring, Book Two, Chapter VII-The Mirror of Galadriel, which describes it thus:
Eärendil, the Evening Star, most beloved of the Elves, shone clear above. So bright was it that the figure of the Elven-lady cast a dim shadow on the ground. 169
Its rays glanced upon a ring about her finger; it glittered like polished gold overlaid with silver light, and a white stone in it twinkled as if the Even-star had come down to rest upon her hand.
It is also said by <PERSON> herself in the same chapter that:
This is Nenya, the Ring of Adamant, and I am its keeper.
These words from <PERSON> could indicate that maybe the white stone in Nenya is indeed the mythical stone Adamant but since it's not written anywhere and <PERSON> have scarcely written anything about Adamant or referring to it in his books we can't know if it's true or not.
Another description of Nenya is give in The Return of the King, Book Six, Chapter IX-The Grey Havens, in which it is described as follows:
...Nenya, the ring wrought of mithril, that bore a single white stone flickering like a frosty star.
Here we learn that Nenya is made of the precious mythical metal mithril which for obvious reasons there are no rings in our world that are wrought of it but the closest metal to mithril besides titanium in our wold according to its descriptions is probably silver with mithril being called also "silver-steel" and "Moria-silver" and even "true-silver" by men although it may not be appropriate for an engagement ring. And again there is a description of a white flickering stone which is likely (although not surely) a diamond or the mythical stone Adamant.
The conclusion is that there is no "correct" design of Nenya according to the books (although there are "incorrect ones" but neither of the depictions that you have presented here falls into this category). However the first design with the flower-like pattern is identical or almost identical to the depiction of <PERSON> in the movies. 652