Bayesian Optimization (BO) is a class of black-box, surrogate-based heuristics that can efficiently optimize problems that are expensive to evaluate and therefore allow only small evaluation budgets. Regardless of the size of the budget, high dimensionality also poses a challenge to BO, whose performance reportedly often suffers when the dimension exceeds 15 variables. Many new algorithms have been proposed to address this problem. However, it is not well understood which one is the best for which optimization scenario. In this work, we compare five state-of-the-art high-dimensional BO algorithms, with vanilla BO and CMA-ES on the 24 BBOB functions of the COCO environment at two dimensionalities, 10 and 60 variables. Our results confirm the superiority of BO over CMA-ES for limited evaluation budgets and suggest that the most promising approach to improve BO at high dimensionality is the use of trust regions. However, we also observe significant performance differences for different function landscapes and budget exploitation phases, indicating improvement potential, e.g., through hybridization of algorithmic components.