Context. Regular spaceborne measurements have revealed that solar brightness varies on multiple timescales, variations on timescales greater than a day being attributed to a surface magnetic field. Independently, ground-based and spaceborne measurements suggest that Sun-like stars show a similar, but significantly broader pattern of photometric variability. Aims. To understand whether the broader pattern of stellar variations is consistent with the solar paradigm, we assess relative contributions of faculae and spots to solar magnetically-driven brightness variability. We investigate how the solar brightness variability and its facular and spot contributions depend on the wavelength, timescale of variability, and position of the observer relative to the ecliptic plane. Methods. We performed calculations with the SATIRE model, which returns solar brightness with daily cadence from solar disc area coverages of various magnetic features. We took coverages as seen by an Earth-based observer from full-disc SoHO/MDI and SDO/HMI data and projected them to mimic out-of-ecliptic viewing by an appropriate transformation. Results. Moving the observer away from the ecliptic plane increases the amplitude of 11-year variability as it would be seen in Stromgren (b+y)/2 photometry, but decreases the amplitude of the rotational brightness variations as it would appear in Kepler and CoRoT passbands. The spot and facular contributions to the 11-year solar variability in the Stromgren (b+y)/2 photometry almost fully compensate each other so that the Sun appears anomalously quiet with respect to its stellar cohort. Such a compensation does not occur on the rotational timescale. Conclusions. The rotational solar brightness variability as it would appear in the Kepler and CoRoT passbands from the ecliptic plane is spot-dominated, but the relative contribution of faculae increases for out-of-ecliptic viewing so that the apparent brightness variations are faculae-dominated for inclinations less than about i=45°. Over the course of the 11-year activity cycle, the solar brightness variability is faculae-dominated shortwards of 1.2µm independently of the inclination.