Using observations from the Coronal Diagnostic Spectrometer (CDS) on SoHO and the Soft X-ray Telescope (SXT) on Yohkoh we investigate how the spatial properties of active region emission observed in the EUV and X-ray range varies with temperature. We examine the contrast per unit area of the EUV emission from a number of active regions, and employ correlation techniques and Fourier methods with which we obtain the two dimensional power spectrum of the intensity distribution for a number of images in emission lines formed at different temperatures. Integrating this over polar angle we find isotropic power-law behaviour at all temperatures in a number of topologically different active regions, with a tendency for flatter spectra at lower temperatures. The existence of power-law spectra indicates that there is no preferred length scale within the regions, at least not a resolvable one, while flatter spectra at lower temperatures indicate that the structures are relatively smaller in this temperature range, possibly providing support for the idea of a multi-component transition region (TR). Implications for various heating models are discussed.