The use of high-gain directional communications is key to enable the capacity enhancement of millimeter-wave (mm-wave) for SG-and-beyond networks. However, robust mm-wave coverage using directional beams entails significant beamsteering effort for maintaining precise beam alignment between the base station and the user. Numerous mm-wave beamsteering algorithms have been proposed in the literature, but verified largely using statistical channel models or limited measurements. Importantly this still leaves open the question of whether these studies can be directly translated to real outdoor mm-wave network deployments. In this paper, we present the results of the first extensive comparative evaluation of eight state-of-the-art mm-wave beamsteering algorithms based on outdoor mm-wave measurements using phased antenna arrays. We collect received signal strength data over fine-grained 3D angular orientations for 78 spatially-dense user positions in a European city, comprising an open-source dataset of over 421,000 individual measurements. We then perform an empirical evaluation of the beamsteering algorithms in the context of link establishment for static and link maintenance for mobile users. Overall, our results show that these state-of-the-art mm-wave beamsteering algorithms, when tested on real measurement data, perform far from optimal and worse than originally reported. A key takeaway from our evaluation is that the practical feasibility of beamsteering algorithms strongly depends on the trade-off between the incurred beam training delay and the antenna gains facilitated in the initial beam training stage which limit the established link budget. Our study of link maintenance for mobile users showed significant deviations from the maximum achievable performance for all algorithms, including those that leverage correlation of the mm-wave sparse link opportunities or historical link information for link recovery. This shows that, to enable seamless connectivity in future mm-wave networks, more sophisticated beamsteering algorithms must be designed that intelligently adapt to the site-specific mm-wave channel while taking into account the realistic antenna beams of commercially-viable phased antenna arrays.