We present an extensive study of the structural, magnetic and thermodynamic properties of high-quality monocrystals of two heterometallic oxyborates from the ludwigite family: Cu2GaBO5 and Cu2AlBO5 in the temperature range above 2 K. The distinctive feature of the investigated structures is the selective distribution of Cu and Ga/Al cations. The unit cell of Cu2GaBO5 and Cu2AlBO5 contains four nonequivalent crystallographic sites of metal ions. Two sites in the structure of Cu2GaBO5 are fully occupied by Cu atoms which form the quasi one-dimensional chains along the a-axis. For Cu2AlBO5 all sites are partially occupied by Al and Cu atoms. The joint analysis of low-temperature data on magnetic susceptibility and magnetic contribution to the specific heat showed that Cu2AlBO5 and Cu2GaBO5 exhibit an antiferromagnetic transition at T-N = 2.4 and 4.1 K, respectively. The magnetic response below T-N can be represented as the sum of two contributions: the ordered component and the paramagnetic contribution from defects of the same relative weight. It is shown that the external magnetic field above 2.5T and 2.8T for Cu2GaBO5 and Cu2AlBO5, respectively, leads to a broadening of the magnetic phase transition indicating suppression of the long-range antiferromagnetic order.