By using state-of-the-art first-principles calculations based on density functional theory (DFT), we conduct a comparative study of the mechanical, electrical, and in-plane thermal transport properties of recently synthesized graphenelike C3B and C3N nanosheets. Our DFT results reveal that the monolayer C3B remarkably possesses a lower elastic modulus and in-plane stiffness as well as ultimate tensile strength compared to C3N, while obviously stronger anisotropy in failure behavior is found in C3B sheets. Both monolayer materials are found as semiconductors with indirect bandgaps of about 1.78 eV and 1.15 eV at the HSE06 level, and their carrier mobilities demonstrate remarkable anisotropy. Additionally, the electron mobility of C3B is found to be much higher than its hole mobility, while for C3N, the reverse is true. For the thermal transport properties, as expected, the intrinsic lattice thermal conductivity of the monolayer C3B (301 W/m K at 300 K) is also lower than that of C3N (380 W/m K at 300 K), while much great anisotropy of in-plane thermal conductivity is found in C3B. The underlying mechanisms governing the phonon thermal transport of these two graphenelike monolayers are thoroughly discussed and compared. Our research will benefit future theoretical research and practical application of these two novel boron-carbide and carbon-nitride materials.