Polyelectrolyte dendrimers attract large interest and find multiple applications in many fields. The majority of theoretical and simulation works consider dendrimers with symmetrical branching where all spacers have the same length. In the present work, we for the first time systematically studied the effect of asymmetry of branching in flexible uniformly charged dendrimers on their structural properties. Lysine dendrimers with lysine amino acid residues as branching units and with spacers consisting of uniformly charged linear lysine (or arginine) peptides of two different lengths are an example of such dendrimers. The Scheutjens-Fleer self-consistent field approach was used to study the dendrimers with different asymmetries of branching and different generation numbers in solution at different salt concentrations. Three regimes - osmotic, salt-dominant, and quasi-neutral - were distinguished, and corresponding theoretical scaling dependencies have been verified. It was demonstrated that large-scale conformational properties practically do not depend on asymmetry of branching, but in the osmotic regime, the gyration radius weakly depends on it. The asymmetry of branching is manifested, however, in the internal structure of dendrimers, such as the radial distributions of monomer units, branching points, and terminal segments. The asymmetry of branching significantly affects also electrostatic properties of the dendrimers in the low-salt regime. While dendrimers with symmetric branching behave as a uniformly charged sphere with the maximum of electrostatic field on its surface, dendrimers with asymmetric branches behave as a sphere with decaying local charge density. The effective radius of an equivalent charged sphere increases and the surface electrostatic potential (ζ-potential) decreases with an increase of asymmetry of branching.