Observations of line of sight (LOS) Doppler velocity and non-thermal line width in the off-limb solar corona are often used for investigating the Alfvén wave signatures in the corona. In this study, we compare LOS Doppler velocities and non-thermal line widths obtained simultaneously from two different instruments, Coronal Multichannel Polarimeter (CoMP) and Hinode/EUV Imaging Spectrometer (EIS), on various off-limb coronal regions: flaring and quiescent active regions, equatorial quiet region, and polar prominence and plume regions observed in 2012-2014. CoMP provides the polarization at the Fe xiii 10747 Å coronal forbidden lines which allows their spectral line intensity, LOS Doppler velocity, and line width to be measured with a low spectral resolution of 1.2 Å in 2-D off limb corona between 1.05 and 1.40 RSun, while Hinode/EIS gives us the EUV spectral information with a high spectral resolution (0.025 Å) in a limited field of view raster scan. In order to compare them, we make pseudo raster scan CoMP maps using information of each EIS scan slit time and position. We compare the CoMP and EIS spectroscopic maps by visual inspection, and examine their pixel to pixel correlations and percentages of pixel numbers satisfying the condition that the differences between CoMP and EIS spectroscopic quantities are within the EIS measurement accuracy: ±3 km s-1 for LOS Doppler velocity and ±9 km s-1 for non-thermal width. The main results are summarized as follows. By comparing CoMP and EIS Doppler velocity distributions, we find that they are consistent with each other overall in the active regions and equatorial quiet region (0.25 ≤ CC ≤ 0.7), while they are partially similar to each other in the overlying loops of prominences and near the bottom of the polar plume (0.02 ≤ CC ≤ 0.18). CoMP Doppler velocities are consistent with the EIS ones within the EIS measurement accuracy in most regions (≥ 87% of pixels) except for the polar region (45% of pixels). We find that CoMP and EIS non-thermal width distributions are similar overall in the active regions (0.06 ≤ CC ≤ 0.61), while they seem to be different in the others (-0.1 ≤ CC ≤ 0.00). CoMP non-thermal widths are similar to EIS ones within the EIS measurement accuracy in a quiescent active region (79% of pixels), while they do not match in the other regions (≤ 61% of pixels); the CoMP observations tend to underestimate the widths by about 20% to 40% compared to the EIS ones. Our results demonstrate that CoMP observations can provide reliable 2-D LOS Doppler velocity distributions on active regions and might provide their non-thermal width distributions.