We report the results of a Sloan Digital Sky Survey-IV eBOSS program to target X-ray sources and mid-infrared-selected WISE AGN candidates in a 36.8 deg$^2$ region of Stripe 82. About half this survey (15.6 deg$^2$) covers the largest contiguous portion of the Stripe 82 X-ray survey. This program represents the largest spectroscopic survey of AGN candidates selected solely by their WISE colors. We combine this sample with X-ray and WISE AGN in the field identified via other sources of spectroscopy, producing a catalog of 4847 sources that is 82% complete to $rsim22$. Based on X-ray luminosities or WISE colors, 4730 of these sources are AGN, with a median sample redshift of $zsim1$. About 30% of the AGN are optically obscured (i.e., lack broad lines in their optical spectra). BPT analysis, however, indicates that 50% of the WISE AGN at $z<0.5$ have emission line ratios consistent with star-forming galaxies, so whether they are buried AGN or star-forming galaxy contaminants is currently unclear. We find that 61% of X-ray AGN are not selected as MIR AGN, with 22% of X-ray AGN undetected by WISE. Most of these latter AGN have high X-ray luminosities ($L_{rm x} > 10^{44}$ erg s$^{-1}$), indicating that MIR selection misses a sizable fraction of the highest luminosity AGN, as well as lower luminosity sources where AGN heated dust is not dominating the MIR emission. Conversely, $sim$58% of WISE AGN are undetected by X-rays, though we do not find that they are preferentially redder than the X-ray detected WISE AGN.
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