Context. Fewer than 1% of all exoplanets detected to date have been characterized on the basis of spectroscopic observations of their atmosphere. Unlike indirect methods, high-contrast imaging offers access to atmospheric signatures by separating the light of a faint off-axis source from that of its parent star. Forthcoming space facilities, such as WFIRST/LUVOIR/HabEX, are expected to use coronagraphic instruments capable of imaging and spectroscopy in order to understand the physical properties of remote worlds. The primary technological challenge that drives the design of these instruments involves the precision control of wavefront phase and amplitude errors. To suppress the stellar intensity to acceptable levels, it is necessary to reduce phase aberrations to less than several picometers across the pupil of the telescope. Aims. Several focal plane wavefront sensing and control techniques have been proposed and demonstrated in laboratory to achieve the required accuracy. However, these techniques have never been tested and compared under the same laboratory conditions. This paper compares two of these techniques in a closed loop in visible light: the pair-wise (PW) associated with electric field conjugation (EFC) and self-coherent camera (SCC). Methods. We first ran numerical simulations to optimize PW wavefront sensing and to predict the performance of a coronagraphic instrument with PW associated to EFC wavefront control, assuming modeling errors for both PW and EFC. Then we implemented the techniques on a laboratory testbed. We introduced known aberrations into the system and compared the wavefront sensing using both PW and SCC. The speckle intensity in the coronagraphic image was then minimized using PW+EFC and SCC independently. Results. We demonstrate that both techniques – SCC, based on spatial modulation of the speckle intensity using an empirical model of the instrument, and PW, based on temporal modulation using a synthetic model – can estimate the wavefront errors with the same precision. We also demonstrate that both SCC and PW+EFC can generate a dark hole in space-like conditions in a few iterations. Both techniques reach the current limitation of our laboratory bench and provide coronagraphic contrast levels of ∼5 × 10⁻⁹ in a narrow spectral band (< 0.25% bandwidth). Conclusions. Our results indicate that both techniques are mature enough to be implemented in future space telescopes equipped with deformable mirrors for high-contrast imaging of exoplanets.