Using coordinated observations of a quiet coronal region, we study the intercalibration of the CDS and EIT instruments on board the Solar and Heliospheric Observatory (SOHO) and the Transition Region and Coronal Explorer (TRACE). We derive the differential emission measure (DEM) distribution from CDS spectral line intensities and convolve it with EIT and TRACE temperature response functions, calculated with the latest atomic data from the CHIANTI database, to predict count rates in their observing channels. We examine different analysis methods and briefly discuss some more advanced aspects of atomic modeling such as the density dependence of the ionization fractions. We investigate the implications for our study using data from the ADAS database. We find that our CDS DEM can predict the TRACE and EIT 171 and 195 Å channel count rates to within 25%. However, the accuracy of the predictions depends on the ionization fractions and elemental abundances used. The TRACE 284 Å and EIT 284 and 304 Å filter predictions do not agree well with the observations, even after taking the contribution from the optically thick He II 304 Å line to the TRACE 284 Å channel into account. The different CDS DEM solutions we derive using different ionization fractions produce fairly similar results: the majority of the CDS line intensities used are reproduced to within 20% with only around one-fifth reproduced to worse than 50%. However, the comparison provides us with further clues with which to explain the discrepancies found for some lines, and highlights the need for accurate equilibrium ionization balance calculations even at low density.