Nanopore force spectroscopy is used to study the unzipping kinetics of two DNA hairpin molecules with a 12 base pair long stem containing two contiguous stretches of six GC and six AT base pairs in interchanged order. Even though the thermodynamic stabilities of the two structures are nearly the same, they differ greatly in their unzipping kinetics. When the GC segment has to be broken before the AT segment, the unfolding rate is orders of magnitude smaller than in the opposite case. We also investigated hairpins with stem regions consisting only of AT or GC base pairs. The pure AT hairpins translocate much faster than the other hairpins, whereas the pure GC hairpins translocate on similar timescales to the hairpins with only an initial GC segment. For each hairpin, nanopore force spectroscopy is performed for different loading rates and the resulting unzipping distributions are mathematically transformed to a master curve that yields the unfolding rate as a function of applied voltage. This is compared with a stochastic model of the unfolding process for the two sequences for different voltages. The results can be rationalized in terms of the different natures of the free energy landscapes for the unfolding process.