Studies of atmospheres of directly imaged exoplanets with high-resolution spectrographs have shown that their characterization is predominantly limited by noise on the stellar halo at the location of the studied exoplanet. An instrumental combination of high-contrast imaging and high spectral resolution that suppresses this noise and resolves the spectral lines can therefore yield higher quality spectra. We study the performance of the proposed HiRISE fiber coupling between the SPHERE and CRIRES+ at the VLT for spectral characterization of directly imaged planets. Using end-to-end simulations of HiRISE we determine the S/N of the detection of molecular species for known exoplanets in $H$ and $K$ bands, and compare them to CRIRES+. We investigate the ultimate detection limits of HiRISE as a function of stellar magnitude, and we quantify the impact of different coronagraphs and of the system transmission. We find that HiRISE largely outperforms CRIRES+ for companions around bright hosts like $\beta$ Pic or 51 Eri. For an $H=3.5$ host, we observe a gain of a factor of up to 36 in observing time with HiRISE to reach the same S/N on a companion at 200 mas. More generally, HiRISE provides better performance than CRIRES+ in two-hour integration times between 50-400 mas for hosts with $H<8.5$ and between 50-800 mas for $H<7$. For fainter hosts like PDS 70 and HIP 65426, no significant improvements are observed. We find that using no coronagraph yields the best S/N when characterizing known exoplanets due to higher transmission and fiber-based starlight suppression. We demonstrate that the overall transmission of the system is in fact the main driver of performance. Finally, we show that HiRISE outperforms the best detection limits of SPHERE for bright stars, opening major possibilities for the characterization of future planetary companions detected by other techniques.