Future space telescope coronagraph instruments hinge on the integration of high-performance masks and precise wavefront sensing and control techniques to create dark holes essential for exoplanet detection. Recent advancements in wavefront control algorithms might exhibit differing performances depending on the coronagraph used. This research investigates three model-free and model-based algorithms in conjunction with either a vector vortex coronagraph or a scalar vortex coronagraph under identical laboratory conditions: pairwise probing with electric field conjugation, the self-coherent camera with electric field conjugation, and implicit electric field conjugation. We present experimental results in narrowband and broadband light from the In-Air Coronagraph Testbed at the Jet Propulsion Laboratory. We find that model-free dark hole digging methods achieve broadband contrasts comparable to model-based methods, and we highlight the calibration costs of model-free methods compared with model-based approaches. This study also reports the first time that electric field conjugation with the self-coherent camera has been applied for simultaneous multi-subband correction with a field stop. This study compares the advantages and disadvantages of each of these wavefront sensing and control algorithms with respect to their potential for future space telescopes.