The answer to this used to be relatively straightforward. Economists were interested in institutions, mostly markets and gaming situations, whereas psychologists were interested in individual factors such as learning, social motivation, and the like. Economists focused on outcomes, whereas psychologists tended to focus more on process. Economics experiments reflected the profession's emphasis on stylized quantitative models, whereas psychology experiments were more interested in capturing real world context.
Recently the lines have begun to blur. There is growing recognition on both sides that understanding institutions means understanding the cognitive bounds and desires of the individual, and understanding individual behavior means understanding the institutional framework it takes place in. Experimental economists are still preoccupied with markets and games, but now recognize the importance of understanding learning and social motivation. Some experimental psychologists have begun to work with the kinds of institutionally clear, game theoretic constructs favored by the economists; at the same time experimental economists increasingly recognize the importance of context.