Centralized v Decentralized

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Yin & Yang; Light & Dark; Pog & Champ
Introduction
When we talk about centralization, we are generally talking about power dynamics in decision-making processes. Historically, most systems have been very centralized, in that a king or a president or a CEO have had most if not all decision-making authority. One of the most incredible innovations of the blockchain, is its ability in allowing decentralized systems to be built from the bottom-up. Without this kind of technology, this would have previously been impossible. To develop greater understanding, let's examine and compare existing centralized structures to the emerging decentralized systems that aim to replace them.
The Bank
Centralized
Banks are corporations that exist with a profit motive. Their business model relies on customers depositing funds that they can leverage to increase the value of their own holdings. This creates fees charged to the customer, smaller and smaller interest rates for depositors and higher and higher interest rates for borrowers. You, as a customer, have no authority to dictate how any of these mechanisms operate.
Further, the bank can deny financial services to a user for all manner of reasons. We see this happen in totalitarian countries and democratic countries alike.
Pros of Centralized Banking
Theoretically, greater capacity to react swiftly to extreme events because of centralized decision making.
Greater control of user identity allows for bad actors to be denied access to funds. (Terrorists, Market Manipulators, etc.) 
If you are burned you could theoretically sue someone. 
Regulated by laws in every country.
Cons of Centralized Banking
Single point of failure. When one bank goes down it can take many banks with it. See 2008 Financial Crisis.
Allows for greater market manipulation by insiders. 
People can be shut out of the financial system arbitrarily.
Profit motive and structure means banks are seldom beholden to their customers.
Low interest rates for depositors; high interest rates for borrowers. 
Subject to political pressures
Require Identification
Decentralized
Today, the very existence of blockchain technology and the rise of DAOs are threatening the very structure of the banking system. 
DAOs disrupt the centralization of institutions and banks alike, by replacing fee-taking middlemen (banks, brokers, custodial exchanges, funds) with immutable code. Without these middlemen, the shareholders of a DAO can directly vote on the direction an organization should take. 
Finally, the actual customers of the organization can set fees and determine interest rates. You, the investor and customer, have the freedom to decide what is done with your own money and a direct perspective to the process, which can supremely elevate your financial decisions. 
Further, because of the anonymous and permissionless nature of the blockchain, it is much harder to restrict people's access to funds. This means anyone with a DeFi wallet can theoretically send and receive money to and from whoever they please.
Pros of DAOS
Empower users with decision making ability.
No discrimination.
Decentralized nature protects the organization from single-failure points.
Absence of middlemen = more revenue distributed directly to stakeholders.
Cons of DAOS
Face the risk of users to collude into getting a majority share of governance
Subject to all the weaknesses of a democracy. (mob rule, move slower than centralized systems, dependent on education of the voters, etc.)
Requires some form of trust in policies and their implementations
Unregulated and risky
The Exchange
Centralized
Exchanges are the marketplaces for trading of all manner of financial instruments. The New York Stock Exchange, the NASDAQ, the London Stock exchange are all examples of traditional financial exchanges. These marketplaces function through the use of brokerage firms who act as market makers. These brokerage firms provide liquidity for exchanges by holding large balance sheets of assets and cash that they use to serve as middlemen transactions.
Centralized exchanges in the context of crypto function in a similar manner, with brokerage and exchange rolled up into one. Some examples include Coinbase, Binance and Kucoin. If it asks for you to confirm your real life identity, it's likely a centralized exchange.
Both have similar weaknesses, in that market makers have undue influence over price action. Market makers can set prices arbitrarily or create artificial scarcity by hoarding assets.
Pros of Centralized Exchanges
Trading can be halted if market is in freefall or cascading liquidations occur. 
Deep Liquidity.
Only way to directly interact with the Fiat money system. 
Regulated by governments.
Cons of Centralized Exchanges
Subject to political pressures.
Markets manipulation. 
Identification Requirements. 
Access can be denied arbitrarily.
Assymetric profit structure that rewards institutions.
High fees for both buyer and seller.
Decentralized
Decentralized exchanges are the backbone of DeFi. They leverage the power of Automated Market Makers (AMM) to eliminate the need for middlemen. An AMM is a series of sophisticated smart contracts that use liquidity pools to conduct trades using a constant product formula. Basically, you become can participate in market making by depositing assets in a pool. Then, just like the brokerage firms, you profit off of the trades. The specific fee percentages and distribution is all handled by the smart contract.
Pros of Decentralized Exchanges
Anyone can participate in trading or market making and collect trading fees. 
Fees are lower as the contract does most of the work. 
Not controlled by any central authority. 
Trades settle very quickly (depending on network the DEX operates on).
Cons of Decentralized Exchanges
Liquidity wars have resulted in unstable liquidity as users chase higher emission rates for pools. 
Cannot bridge Fiat directly.
Unregulated. 
Smaller liquidity pools can be subject to whale manipulation.
Conclusion
Traditional, centralized finance has been around for a very long time and has deep ties to the political and societal institutions around us. On the other hand, decentralized finance is in its infancy and operates outside the constraints of institutions that have built the world we live in today. This makes for very interesting times as vested interests must compete against a quickly developing technology. The advantages and disadvantages to both make neither entirely superior to the other. Centralized structures provide the stability to conduct many real world transactions that are not possible via DeFi. While DeFi's flexibility offers a level of economic freedom not possible in legacy systems.
It is important for us all to be mindful of these differences as we interact with these systems and to be aware that they continue to shape and direct each other even as they compete.
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Introduction
The Bank
The Exchange
Conclusion