  We establish that constructive continued fraction dimension originally
defined using $s$-gales is robust, but surprisingly, that the effective
continued fraction dimension and effective (base-$b$) Hausdorff dimension of
the same real can be unequal in general.
  We initially provide an equivalent characterization of continued fraction
dimension using Kolmogorov complexity. In the process, we construct an optimal
lower semi-computable $s$-gale for continued fractions. We also prove new
bounds on the Lebesgue measure of continued fraction cylinders, which may be of
independent interest.
  We apply these bounds to reveal an unexpected behavior of continued fraction
dimension. It is known that feasible dimension is invariant with respect to
base conversion. We also know that Martin-L\"of randomness and computable
randomness are invariant not only with respect to base conversion, but also
with respect to the continued fraction representation. In contrast, for any $0
< \varepsilon < 0.5$, we prove the existence of a real whose effective
Hausdorff dimension is less than $\varepsilon$, but whose effective continued
fraction dimension is greater than or equal to $0.5$. This phenomenon is
related to the ``non-faithfulness'' of certain families of covers, investigated
by Peres and Torbin and by Albeverio, Ivanenko, Lebid and Torbin.
  We also establish that for any real, the constructive Hausdorff dimension is
at most its effective continued fraction dimension.
