Biiiiiig difference. :)
"Clients like you... should be getting out of debt" sounds like an accusation. It's very direct. You're pointing a finger at me. Formal/business English is very tactful, and far less direct.
"Clients like yourself... should be getting out of debt" sounds more respectful an polite, as if you thought about their situation. You're offering me tea, and cake. It's slightly more roundabout, and less blunt.