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

Effective Continued Fraction Dimension versus Effective Hausdorff Dimension of Reals