Laser-wakefield acceleration is a promising technique for the next generation of ultra-compact, high-energy particle accelerators. However, for a meaningful use of laser-driven particle beams it is necessary that they present a high degree of pointing stability in order to be injected into transport lines and further acceleration stages. Here we show a comprehensive experimental study of the main factors limiting the pointing stability of laser-wakefield accelerated electron beams. It is shown that gas-cells provide a much more stable electron generation axis, if compared to gas-jet targets, virtually regardless of the gas density used. A sub-mrad shot-to-shot fluctuation in pointing is measured and a consistent non-zero offset of the electron axis in respect to the laser propagation axis is found to be solely related to a residual angular dispersion introduced by the laser compression system and can be used as a precise diagnostic tool for compression oprtimisation in chirped pulse amplified lasers.