In this work, we studied amorphous carbon ($a$-C) thin films deposited using direct current (dc) and high power impulse magnetron sputtering (HiPIMS) techniques. The microstructure and electronic properties reveal subtle differences in $a$-C thin films deposited by two techniques. While, films deposited with dcMS have a smooth texture typically found in $a$-C thin films, those deposited with HiPIMS consist of dense hillocks surrounded by a porous microstructure. The density of $a$-C thin films is a decisive parameter to judge their quality. Often, x-ray reflectivity (XRR) has been used to measure the density of carbon thin films. From the present work, we find that determination of density of carbon thin films, specially those with a thickness of few tens of nm, may not be accurate with XRR due to a poor scattering contrast between the film and substrate. By utilizing neutron reflectivity (NR) in the time of flight mode, a technique not commonly used for carbon thin films, we could accurately measure differences in the densities of $a$-C thin films deposited using dcMS and HiPIMS.