It is probably, by now, quite visible to one and all that Artanis is in a world very different from her own. However, in exactly how different that world is, I have perhaps extrapolated from the information which we have been given. In my mind, the Valinorian Elves have become hunter/foragers, sedentary and with established power structures but pre-agriculture and without monetary systems.
The Elves in Valinor can be considered to be in a semi-Edenistic state, whereby the Kinslaying -- seen at the end of the time from which Artanis is taken -- is a 'fall' common to mythology and parallels in the Bible with Cain and Abel. Although the comparison can not be taken utterly literally (for example, the Elves are capable of metalworking, which does not appear in the Bible for some generations), it does introduce some interesting points.
Firstly, it supports the idea of equality between the sexes of Elves -- it was not until Adam and Eve were cast out of Eden that "emnity" was cast between them and that Eve was told that Adam would "rule over" her. Adding this to other factors seen within Tolkien's Elves (that Artanis was one of the leaders of the Host of the Noldor, that there are equal Valar and Valier, that the women mentioned by name have their own rights within stories) it can be surmised that, at least before the Kinslaying, there was not major gendered inequality. Interestingly, it is after the move into Endor that Aredhel (Artanis' first cousin, and the only other granddaughter of Finwë) is forced into marriage. Whilst this issue is clearly not entirely resolved in terms of equality, it is also worth remembering that the text on which this is based is rather outdated.
As a side note, I'm fairly sure that I've read somewhere that male Elves liked cooking. Also that male Elves were better with magic suited to battle, whilst female Elves tended towards healing. However, I'm not sure whether this latter statement is actually true to Tolkien's work (consider Elrond the healer, or Artanis's role in the Flight of the Noldor). To be honest, I'm not sure that I buy it. Add in some androgyny in terms of a lack of facial hair and physical strength that doesn't require overt musculature, and it's easy to see a much greater equality than pictured in, for example, Stone Age human populations.
Way more to come, honest! Feel free to comment/question/argue~