We present a measurement of R-K(), the branching fraction ratio B(B -> K mu(+)mu(-))/B(B -> K* e(+) e(-)), for both charged and neutral B mesons. The ratio for the charged case RK*+ is the first measurement ever performed. In addition, we report absolute branching fractions for the individual modes in bins of the squared dilepton invariant mass q(2). The analysis is based on a data sample of 711 fb(-1), containing 772 x 10(6) B (B) over bar events, recorded at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. The obtained results are consistent with standard model expectations.