Would you say customer/client referral programs work better in large or small companies? Or does size even matter?

For services firms, having a referenceable client is the goal of any project; similarly for products, having a satisfied customer that will "rave" about the product and recommend others to use is a goal mine. In terms of large / small companies, the line of sight to the customer experience is "shorter" in smaller companies (all things equal), so the positive feedback from the products/services can be leveraged more quickly. In contrast, if the organization culture is not open and prevents information flow etc, then size doesn't matter as program success is impeded by virtue of the obstacles.

Size has no bearing. It is a common sales tactic to ask for referrals from your customers/cllents. A strategy that I have used quite successfully in the past is to send out a Customer Satisfaction survey. The last question of the survey states, "If you feel that anyone else would benefit from our products or services, please let us know___________________________________________" About 25% of the respondents will give you a name, if they were satisfied.