  Using improved theoretical calculations of the decay form factors in the
Light Cone-QCD sum rule approach, we investigate the decay rates, dilepton
invariant mass spectra and the forward-backward (FB) asymmetry in the decays $B
\to (K,K^*) \ell^+ \ell^-$ ($\ell^\pm =e^\pm,\mu^\pm,\tau^\pm$) in the standard
model (SM) and a number of popular variants of the supersymmetric (SUSY)
models. Theoretical precision on the differential decay rates and FB-asymmetry
is estimated in these theories taking into account various parametric
uncertainties. We show that existing data on $B \to X_s \gamma$ and the
experimental upper limit on the branching ratio ${\cal B}(B \to K^* \mu^+
\mu^-)$ provide interesting bounds on the coefficients of the underlying
effective theory. We argue that the FB-asymmetry in $B \to K^* \ell^+ \ell^-$
constitutes a precision test of the SM and its measurement in forthcoming
experiments may reveal new physics. In particular, the presently allowed
large-$\tan \beta$ solutions in SUGRA models, as well as more general
flavor-violating SUSY models, yield FB-asymmetries which are characteristically
different from the corresponding ones in the SM.
