Multi-fidelity surrogate models combining dimensionality reduction and an intermediate surrogate in the reduced space allow a cost-effective emulation of simulators with functional outputs. The surrogate is an input-output mapping learned from a limited number of simulator evaluations. This computational efficiency makes surrogates commonly used for many-query tasks. Diverse methods for building them have been proposed in the literature, but they have only been partially compared. This paper introduces a unified framework encompassing the different surrogate families, followed by a methodological comparison and the exposition of practical considerations. More than a dozen of existing multi-fidelity surrogates have been implemented under the unified framework and evaluated on a set of benchmark problems. Based on the results, guidelines and recommendations are proposed regarding multi-fidelity surrogates with functional outputs. Our study shows that most multi-fidelity surrogates outperform their tested single-fidelity counterparts under the considered settings. But no particular surrogate is performing better on every test case. Therefore, the selection of a surrogate should consider the specific properties of the emulated functions, in particular the correlation between the low- and high-fidelity simulators, the size of the training set, the local nonlinear variations in the residual fields, and the size of the training datasets.