The numerical implementation of the linearized gyrokinetic and drift-kinetic improved Sugama (IS) collision operators, recently introduced by Sugama et al. [Phys. Plasmas 26, 102108 (2019)], is reported. The IS collision operator extends the validity of the widely used original Sugama (OS) operator [Sugama et al., Phys. Plasmas 16, 112503 (2009)] to the Pfirsch-Schluter collisionality regime. Using a Hermite-Laguerre velocity-space decomposition of the perturbed gyrocenter distribution function that we refer to as the gyro-moment approach, the IS collision operator is written in a form of algebraic coefficients that depend on the mass and temperature ratios of the colliding species and perpendicular wavenumber. A comparison between the IS, OS, and Coulomb collision operators is performed, showing that the IS collision operator is able to approximate the Coulomb collision operator in the case of trapped electron mode in H-mode pedestal conditions better than the OS operator. In addition, the IS operator leads to a level of zonal flow residual which has an intermediate value between the Coulomb and the OS collision operators. The IS operator is also shown to predict a parallel electrical conductivity that approaches the one of the Coulomb operator within less than 1%, while the OS operator can underestimate the parallel electron current by at least 10%. Finally, closed analytical formulas of the lowest order gyro-moments of the IS, OS, and Coulomb operators are given, which are ready to use to describe the collisional effects in reduced gyro-moment fluid models. Published under an exclusive license by AIP Publishing.