The Lagrange and Markov spectra encode the best constants in Diophantine approximation for irrational numbers and infimum of binary quadratic forms. Markov proved in 1880 that below 3 the two spectra coincide and form a discrete set accumulating only at 3, and it is known that their Hausdorff dimensions agree and become positive immediately above this threshold. We derive several results that quantify this transition. For example, using counting arguments of Sturmian words, we obtain an explicit approximation of this Hausdorff dimension function near 3, which is essentially optimal for C² functions. We further prove that the Lagrange and Markov spectra cease to coincide immediately above 3, by establishing quantitative lower bounds on the Hausdorff dimension of their difference set near 3.