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We present a comparison of high-resolution images of the solar surface taken in the Mg II k and Ca II H channels of the Filter Imager on the balloon-borne solar observatory SUNRISE. The Mg and Ca lines are sampled with 0.48 nm and 0.11 nm wide filters, respectively. The two channels show remarkable qualitative and quantitative similarities in the quiet Sun, in an active region plage and during a small flare. However, the Mg filtergrams display 1.4-1.7 times higher intensity contrast and appear more smeared and smoothed in the quiet Sun. In addition, the fibrils in a plage are wider. Although the exposure time is 100 times longer for Mg images, the evidence suggests that these differences cannot be explained only with instrumental effects or the evolution of the solar scene. The differences at least partially arise because of different line-formation heights, the stronger response of Mg k emission peaks to the higher temperatures, and the larger height range sampled by the broad Mg filter used here. This is evidently manifested during the flare when a surge in Mg evolves differently than in Ca. [ABSTRACT FROM AUTHOR]