To show the importance of high-spatial resolution observations of HII regions when compared with observations obtained with larger apertures such as ISO, we present mid-infrared spectra of two Magellanic Cloud HII regions, N88A and N160A. We obtained mid-infrared (8-13 um), long-slit spectra with TIMMI2 on the ESO 3.6m 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. Concerning N88A, an isolated HII 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 HII region of about 3 arcsec in diameter. This is not the case for N160A, which has a more complex morphology. We have spectroscopically isolated for the first time the individual contributions of the three components of N160A, two high-excitation blobs, A1 and A2, and the young stellar object N160A-IR. In addition, extended [SIV] 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 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.