Because thermal conductivity of carbon nanomaterials is inevitably lowered upon functionalization and functionalization is required to stabilize nanofluids, to meet the two criteria of thermal conductivity enhancement and homogeneous dispersion over time is still highly challenging for carbon nanomaterial based nanofluids. In this work, both multiwalled carbon nanotubes and graphene nanoplatelets have been covalently functionalized with different rates by refluxing in sulfuric acid/nitric acid of different concentrations (1, 3, 5 and 7 M). We show that a compromise can be found between thermal conductivity enhancement of carbon-based nanofluids (to maximize) and carbon structure damaging through functionalization (to minimize) while a stable dispersion is obtained. An in-depth characterization by transmission electron microscopy, Raman spectroscopy, Fourier transformed Infra-red spectroscopy, thermogravimetry analysis and thermogravimetry analysis coupled to a mass spectrometer allow to evaluate both the applied functionalization efficiency and the structural damage undergone by each carbon nanomaterial. From the prepared nanofluids at 0.25 wt% concentration, the best performance is achieved with MWCNT treated by an acid mixture of H2SO4/HNO3 (1:1 volumetric proportion) at concentrations of 3 and 5 M where the thermal conductivity reaches an enhancement of 9.4 % at 20 °C and a dispersion stability over 5 weeks with no change in nanofluid absorbance. We have proved that the proposed approach allows to meet the two key criteria strongly desired for nanofluid design, leading to nanofluids with higher performances compared to other nanofluids prepared with carbon nanotubes treated with similar methods from the oxidized carbon nanotube family.