We present a census of the population of deeply embedded young stellar objects (YSOs) in the Ophiuchus molecular cloud complex based on a combination of Spitzer Space Telescope mid-infrared data from the "Cores to Disks" (c2d) legacy team and JCMT/SCUBA submillimeter maps from the COMPLETE team. We have applied a method developed for identifying embedded protostars in Perseus to these datasets and in this way construct a relatively unbiased sample of 27 candidate embedded protostars with envelopes more massive than our sensitivity limit (about 0.1 M_sun). Embedded YSOs are found in 35% of the SCUBA cores - less than in Perseus (58%). On the other hand the mid-infrared sources in Ophiuchus have less red mid-infrared colors, possibly indicating that they are less embedded. We apply a nearest neighbor surface density algorithm to define the substructure in each of the clouds and calculate characteristic numbers for each subregion - including masses, star formation efficiencies, fraction of embedded sources etc. Generally the main clusters in Ophiuchus and Perseus (L1688, NGC1333 and IC348) are found to have higher star formation efficiencies than small groups such as B1, L1455 and L1448, which on the other hand are completely dominated by deeply embedded protostars. We discuss possible explanations for the differences between the regions in Perseus and Ophiuchus, such as different evolutionary timescales for the YSOs or differences, e.g., in the accretion in the two clouds. ; Comment: Accepted for publication in ApJ (56 pages, 13 figures; abstract abridged). Version with full-resolution figures available at http://www.astro.uni-bonn.de/~jes/paper120.pdf