A comparative dynamic Monte Carlo simulation study of polydisperse living polymer brushes, created by surface-initiated living polymerization, and conventional polymer monodisperse brush, comprising linear polymer chains, grafted to a planar substrate under good solvent conditions, is presented. The living brush is created by end-monomer (de)polymerization reaction after placing an array of initiators on a grafting plane in contact with a solution of initially nonbonded segments (monomers). At equilibrium, the monomer density profile phi(z) of the LPB is found to decline as phi(z) alpha z(-a) with the distance from the grafting plane z, while the distribution of chain lengths in the brush scales as c(N) alpha N-tau. The measured values alpha approximate to 1 0.64 and tau approximate to 1.70 are very close to those predicted within the framework of the diffusion -limited aggregation theory, alpha = 2/3 and tau = 7/4. At varying mean degree of polymerization (from < L > = 28 to < L > = 170) and effective grafting density (from sigma(g) = 0.0625 to sigma(g) = 1.0), we observe a nearly perfect agreement in the force-distance behavior of the simulated LPB with own experimental data obtained from colloidal probe AFM analysis on PNIPAAm brush and with data obtained by Plunkett et al. [Langmuir 2006, 22, 4259] from SFA measurements on the same polymer.