Business strategy between single and diversified corporations will differ. The differences will revolve around branding, risk and corporate institutionalism.
A single business corporation must focus a large part of their business strategy on branding their company or product. If the business has a single product or service it is important for them to advertise the product to gain market share. The single business motto might be along the lines of "trust us because we do this one service better than anyone". A diverse corporation does not need to focus entirely on one product, but can emphasis their size. They might use the motto "trust us because we offer a variety of services". Coca-Cola is an example of the diversification model. There are many types of cola brands that are subsidiaries of Coca-Cola. The main corporation does not care which brand you choose, because the revenue all goes to the company.
Another difference is the amount of risk any marketing or strategic move each entity can afford. A single business entity must be more considerate of decisions because it cannot afford the same amount of risk. A diversified entity can introduce a riskier new product or marketing campaign because it has additional businesses or brands to hedge against a poor decision. Riskier investments can have large rewards and are typically seen in larger companies able to absorb revenue decreases.
Corporate institutionalism is one area a single business entity has an advantage. It is easier for a single entity to instill a company culture than a diversified entity. The simpler model places all of the employees on the same general goal; to promote the single product or service. A diversified entity will have many different missions, products or services to promote. This dilutes the motivation across different areas and may create tension as units compete for resources.