Really, what's the difference between a city elf and a poor human other than slender bodies and pointy ears?
What's the difference between a poor Jew and a poor Christian apart from how one's not supposed to eat pork?
Apart from the obvious "religious difference," there is historical and cultural differences. Different traditions and customs.
City elves may have long lost touch with their religion and may be losing touch with their history, traditions and customs, but they still have a distinctly elven historical and cultural identity. Elves everywhere have a shared historical identity of knowing they were once free, then enslaved by humans, then freed by Andraste, then got their own land, then lost their land again and now live under or away from humans humans. They are a race of people who were once autonomous and now aren't, and that shared knowledge affects individuals and communities, in a way it can't for humans.
As a culture, the elves are also much more community-centered than the humans. Go into the alienage and most elves will know everyone else whereas most humans probably won't. (Look at the difference between the community involvement of the Denerim and Kirkwall Alienage compared to the community involvement of, say, Lowtown.) Elves culturally view everyone in their alienage or clan as their family (this applies to both city elves and Dalish). In the City Elf Origin, everyone you meet is referred to as family, even if they aren't necessarily blood-related. Humans only regard immediate blood relatives as family (parents, siblings, aunts/uncles, nieces/nephews), and don't care much about the goings on of others.
The elves also place greater value on community over individuality. Whether Dalish Clan or a City Alienage, most elves are more community-centered; more value is placed on the overall well-being of the community, and decisions and actions that help the community are praised whereas those that abandon or harm them are looked down on. Humans, on the other hand, are very individualistic. Cousland or Hawke can go to help the advancement of #1 and there's no social pressure or reminder to help others or remember where they came from.
EDIT: City Elves also have a Hahren; a community elder who acts as a leader and figure of wisdom, guidance, settles disputes between elves, acts as an emissary to the local human garrison, and so on. Most human neighborhoods, cities and towns don't necessarily have a village elder or wise one who guides the people the way city elves do with Hahrens, or Dalish do with Keepers. Just the act of having a Hahren, an elder, also shows a cultural value in tradition and remembrance. Again, not a cultural value found in human communities.
There is a difference and I won't believe differently.