In tracing the history of the word client back to its Latin root, the Romans used it in the context of a client being someone who needed the protection (legal, financial, etc.) of a patron.
So, the word implies that you and the client are not equals. The client is someone inferior to you. Almost someone you feel sorry for.
I prefer customer because it is more of an equalizing term. The customer and I are equals, collaborators, accustomed to doing business with one another.
In the end, it's whatever you feel comfortable doing. Although, I do enjoy having the conversation with customers about why I use that word instead of client. They seem to be happy that I've thought it through that far...it ends up being another connection point.