We present spectra for a sample of 14 FUors and two T Tauri stars observed with Spitzer or ISO. Based on the appearance of the 10 μm silicate feature, we define two categories of FUors. Objects showing the silicate feature in absorption (Category 1) are still embedded in a circumstellar envelope. The shape of the silicate bands is in good agreement with typical dust compositions of the ISM. Only one object appears too rich in amorphous pyroxene dust, but a superposed emission feature can explain the observed shape. We derive optical depths and extinction values from the silicate and additional ice bands. Particularly, the analysis of the CO₂ ice band at 15.2 μm allows us to search for evidence for ice processing and to constrain whether the absorbing material is physically linked to the central object. For objects showing the silicate band in emission (Category 2), we argue that the feature comes from the surface layer of accretion disks. We find evidence that grain growth has already taken place within the disks, but no clear indications for crystallization are present. We discuss how these observations fit into the picture of a young and active accretion disk. Finally, a framework is proposed how the two categories of FUors can be understood in a general paradigm of the evolution of young, low-mass stars. As one object (Parsamian 21) shows PAH emission features typical for evolved stars, we question its status as a FUor. Additionally, two spectra (RNO 1B and L1551 IRS 5) show [Fe II] emission lines that are attributed to hot, dense, or shocked material related to outflows.