An economy in which deposit-taking banks of a Diamond/ Dybvig style and an asset market coexist is modelled. Firstly, within this framework we characterize distinct financial systems depending on the fraction of households with direct investment opportunities that are less efficient than those available to banks. With this fraction comparatively low, the evolving financial system can be interpreted as market-oriented. In this system, banks only provide efficient investment opportunities to households with inferior investment alternatives. Banks are not active in the secondary financial market nor do they provide any liquidity insurance to their depositors. Households participate to a large extent in the primary as well as in the secondary financial markets. In the other case of a relatively high fraction of households with inefficient direct investment opportunities, a bank-dominated financial system arises, in which banks provide liquidity transformation, are active in secondary financial markets and are the only player in primary markets, while households only participate in secondary financial markets. Secondly, we analyze the effect a run on a single bank has on the entire financial system. Interestingly, we can show that a bank run on a single bank causes contagion via the financial market neither in market-oriented nor in extremely bank-dominated financial systems. But in only moderately bank-dominated (or hybrid) financial systems fire sales of long-term financial claims by a distressed bank cause a sudden drop in asset prices that precipitates other banks into crisis.