Being able to seamlessly deal with complex crack patterns like branching, merging and even fragmentation, phase-field models (PFMs) are promising in the computational modeling of fracture of solids. There are, however, some unclear issues such as (i) are phase-field models mesh-bias objective? and (ii) what value should be selected for the length scale parameter? This manuscript provides answers to these practical questions. Three popular PFMs for brittle and cohesive fracture in the literature are selected, implemented within a single code and used to study the sensitivity to the length scale parameter and the mesh alignment of the solutions to various brittle and quasi-brittle fracture problems with/without singularities and notches. The findings are useful to researchers and engineers who need to perform fracture simulations using a phase-field model.