This article presents a comparative analysis of Ethereum (ETH) market efficiency priced in Bitcoin (BTC), Dai (DAI), and Tether (USDT). The investigation encompasses data obtained from both UNISWAP-V2, a decentralized app utilizing liquidity pools for cryptocurrency pricing, and Binance, a centralized exchange. The study employs a rolling window procedure to apply the MF-DFA, utilizing 256, 384, and 512 observation window sizes. The efficiency of exchange pairs is ranked using the market deficiency measure (MDM). Our findings align with existing literature, revealing an efficiency increase with larger rolling window sizes across centralized and decentralized exchanges. Notably, ETH priced in BTC, DAI, and USDT in decentralized exchanges demonstrates greater efficiency than centralized exchanges for window sizes of 384 and 512 observations. At 256 observations, this efficiency is exclusive to BTC pricing. To delve deeper into this phenomenon and explore the dynamics between distinct pricing mechanisms, the Thermal Optimal Path is employed. The analysis highlights a lead-lag relationship between ETH prices in centralized and decentralized exchanges. The results suggest that market efficiency emerges first in the decentralized exchange, particularly when ETH is priced in BTC. This analysis is crucial for enhancing our understanding of evolving financial ecosystems, guiding regulatory considerations, and empowering market participants to navigate the complexities of both decentralized and centralized trading environments.