I was taught back in grad school (ages ago) that "patient" connotes a power differential where the "doctor" is in a superior role. The argument presented back then was that thinking in terms of "doctor" and "patient" encourages the individual seeking professional services to adopt a passive role where they sit back and wait for the "doctor" to cure them. It was argued that using the term "client" establishes a more egalitarian relationship where the individual seeking services and the professional providing services are on more of an equal footing and it is easier to get the "client" to be an active participant in therapy rather than being a passive recipient.

In reality, my bet is that there isn't one "right" answer to this one. In print, both terms get used. Personally, I lean towards "client" when I'm writing. However, I rarely use either with clients/patients. Typically, I address people by name and, when I need to refer to other clients/patients, I generally use a phrase like "the other people I work with."

It is important to treat those seeking our services with compassion and respect, to actively involve them in treatment, and to remember that professional training may make me more knowledgeable in some areas but does not make me superior to others. I'm not sure it makes a big difference if we use "patient" or "client."