This quote can make sense either way.

If he said "either" it indicates that he feels connected to the person as a friend and also views them as family because that is what they became in their time together on the island.

If he said "neither" then he did not view them as friend or family but still had a very strong connection to them from being on the island together. This could easily apply to: Ben, Locke, or Michael.

I think that Jack was mourning the loss of the person in the casket, not from an emotional loss point of view.....but, rather because he wants to go back to the island and fix things, but needs all of the original losties in order to do that. So, everyone that dies makes that more of an impossibility.