[fhrzxhhc] Distribution of exactly 2 prime factors

Of all n-bit numbers with exactly two prime factors, for a given n, what is the distribution of factor sizes?  Is most of the mass at nearly equal sizes?

Motivation was supposing the hypothetical invention of a factoring algorithm that works well only if the factors are nearly the same size, i.e., the current construction of RSA numbers.  X^2-N^2 trying small values of N already exists, though in the same class as trial division.  We imagine a sophistication.