Aims: To show the importance of high-spatial resolution observations of H II regions when compared with observations obtained with larger apertures such as ISO, we present mid-infrared spectra of two Magellanic Cloud H II regions, N88 A and N160 A. Methods: We obtained mid-infrared (8-13 μm), long-slit spectra with TIMMI2 on the ESO 3.6 m telescope. These are combined with archival spectra obtained with the Infrared Spectrograph (IRS) onboard the Spitzer Space Telescope, and are compared with the low-spatial resolution ISO-SWS data. An inventory of the spectra in terms of atomic fine-structure lines and molecular bands is presented. Results: Concerning N88 A, an isolated H II region with no adjacent infrared sources, the observations indicate that the line fluxes observed by ISO-SWS and Spitzer-IRS come exclusively from the compact H II region of about 3´´ in diameter. This is not the case for N160 A, which has a more complex morphology. We have spectroscopically isolated for the first time the individual contributions of the three components of N160 A, two high-excitation blobs, A1 and A2, and the young stellar object (YSO) N160 A-IR. In addition, extended [S IV] emission is observed with TIMMI2 and is most likely associated with the central star cluster located between A1 and A2. We show the value of these high-spatial resolution data in determining source characteristics, such as the degree of ionization of each high-excitation blob or the bolometric luminosity of the YSO. This luminosity (2×105 L_&sun;) is about one order of magnitude lower than previously estimated. For each high-excitation blob, we also determine the electron density and the elemental abundances of Ne, S, and Ar.