This study investigates whether the macroscopic statistical maturity of cryptocurrencies implies dynamical equivalence with traditional equity markets. We analyze high-frequency data (2020--2025) using the Complexity--Entropy Causality Plane (CECP) and directed horizontal visibility graphs (directed HVG) to uncover complex temporal patterns and time-directed structures in the return series. While conventional stylized facts show striking convergence across all assets, structural diagnostics reveal a compelling paradox: cryptocurrencies appear more locally random than the equity benchmark during ordinary periods, yet exhibit significantly stronger directional time-irreversibility around high-visibility return events. The absolute-return results show that large cryptocurrency fluctuations tend to begin abruptly and remain elevated afterward. Separate analyses of positive returns and negative-return magnitudes show that this pattern is shared across cryptocurrencies on the upside but varies across assets on the downside. We conclude that statistical maturity is only skin-deep; the underlying dynamical processes of mature cryptocurrencies remain fundamentally distinct from traditional benchmarks.
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