The following papers discuss this extensively with numerical experiments, but they tackle specific examples. Emphasis is mine.
This is a comparison of the two techniques using the example of unit commitment, answering your first question.
A popular impression has arisen that the robust approach, with its focus on the worst case, is better able to control risk while stochastic programming emphasizes expected values. However, the stochastic programming formulation can easily accommodate a risk measure. Moreover, the results of both methods depend strongly on the model for the uncertain parameters—either the uncertainty set or the probabilistic scenarios employed in the optimization. [...]
[...] By incorporating risk in the stochastic programming formulation in terms of CVaR with a sufficiently low tail probability, the stochastic programming formulation can achieve the most efficient combinations of cost and risk when a decision maker emphasizes cost. However, when a higher level of conservatism is preferred, robust optimization models can achieve the most efficient combinations of cost and risk. Between the two uncertainty set formulations for robust optimization, the data-driven method that incorporates probabilities of scenarios as well as their ranges of values achieves better cost-risk trade-offs than the one based on ranges alone when the risk parameter is set to its most stringent value.
This is a comparison of the two techniques using the example of a standard transportation problem. This answers the reverse of your first question (i.e. robust optimisation in favour of stochastic programming) which you may find useful. From the abstract,
The proposed robust formulations have the advantage to be solvable in polynomial time and to have theoretical guarantees for the quality of their solutions, which is not the case for the stochastic formulation. Numerical experiments show that the robust approach results in larger objective function values than the stochastic approach due to the certitude of constraints satisfaction and more conservative decision strategies on the number of booked vehicles. Conversely, the computational complexity is higher for the stochastic approach.
 Kazamzadeh, N., Ryan, S. M., Hamzeei, M. (2017). Robust optimization vs. stochastic programming incorporating risk measures for unit commitment with uncertain variable renewable generation. Energy Syst. 10:517-541.
 Maggioni, F., Potra, F. A., Bertocchi, M. (2014). Stochastic versus Robust Optimization for a Transportation Problem. Available from: http://www.optimization-online.org/DB_FILE/2015/03/4805.pdf. [Accessed 13 August 2019].