To the casual observer, the difference between a centralized and a decentralized exchange might not be immediately obvious. Put simply, Binance, Coinbase pro, Kraken and Okex are among the most popular platforms for trading crypto — and all operate a ‘centralized’, clearing house style system where a single organization manages the flow of operations on the exchange. This means that user data is stored on single servers, as opposed to being distributed across multiple ledgers on a public blockchain.
In contrast, decentralized exchanges (DEXs) like Bancor, IDEX and ETHerdelta, offer peer-to-peer or order book-based, non-custodial, trustless exchange solutions. They conduct trades on the blockchain, so parties to a trade exchange assets directly, eliminating the need for a central party to hold client funds.
With user data spread across multiple data points, DEXs have obvious security advantages over centralized exchanges, and also offer a number of other potentially significant advantages.

Users retain custody of their own funds and do not have to leave their crypto in the wallets of centralized exchanges

Users retain anonymity and don’t have to complete the KYC steps required by most centralized exchanges.

Trading fees are generally dependent on gas fees, and are not controlled by the business models of a centralized exchange.

In spite of these advantages BNC exchange data analysis shows that DEXs are only conducting a fraction of the trades of their centralized counterparts. Trading data from six major centralized exchanges (Binance, Bitfinex, Bithumb HitBTC, Huobi and OKEX) was compared to that from nine leading decentralized exchanges (Bancor Network, BitShares, DDEX, ETHerDelta, ForkDelta, IDEX, OpenLedger, StellarTerm, and the Waves Platform)

 
For a period between 1/06/2017 and 31/07/2018, 24 hour volume data for each of the exchanges shows that despite some steady growth shown by a number of DEX’s (Waves, for example, handled 16% more volume from the first day tracked to the last), the volumes handled by decentralized exchanges is dwarfed by that of centralized exchanges.  

 
Binance, the world’s largest exchange by trading volume is centralized. It handles more volume in 24 hours, for example,  than Bancor and Waves, handle in 30 days.

24hr volume indicates the USD value for number of tokens traded on an exchange in a 24 hour period (UTC times used). Numbers are extremely large thus the ‘E+..’ notation  is used in most cases. I.e. 7.91+E14 equals ~$791000000000000.
As this tweet illustrates, for some crypto advocates there is clearly a hope that decentralized exchanges will emerge from the shadows to save crypto traders from some of the cavalier operations undertaken by centralized exchanges. As noted, DEX’s deliver a number of compelling advantages — so why aren’t users flocking to them? 
  
The importance of ‘user experience’
For the average retail investor/crypto trader, exchange hacks are rare enough that they are not really on anybody’s rADAr. Additionally, since the Mt Gox breach, any exchanges that have been hacked have typically replaced any funds lost by users, thereby negating much of the fear-factor that might have driven somebody to a DEX.
Furthermore, centralized exchanges like Binance and Coinbase continue to make strides in user interface, customer support and liquidity solutions. 
For example, Coinbase offer on-ramps into crypto with fiat pairings, have built-in digital wallets, offer brokerage, banking & retail solutions, and in essence have turned themselves into a one-stop shop for anyone looking to engage with crypto.
Perhaps the biggest issue facing DEXs may be the price slippage and liquidity. Slippage occurs when delays in order settlement can affect the price users pay for their trades (up or down). Addressing this is a challenge for DEXs for a number of reasons, but it’s primarily a numbers game — there simply aren’t enough traders using them.Centralized exchanges also frequently offer traders high volume discounts, as well as institutional-grade information tools like charting, and margin trading (trading using credit).  The big exchanges are able to do so because they have the cash to spend on improving their user experience. Binance, for example, is expecting to turn a billion dollar profit this financial year, giving them a market advantage that, from the perspective of a low fee decentralized exchange, appears all but uNASsailable.
The future of DEX solutions
There is reason to be optimistic about the future of decentralized exchanges, however, as advances like the 0x protocol could enable DEXs to offer solutions comparable to centralized exchanges.
With 0x, market making, and buyer & seller interactions occur off-chain, before transaction settlement occurs on-chain. Exchanges operating using 0x (called ‘relayers’), can thus offer more complex revenue models through schemes like fee splitting with other exchanges using 0x, reserve manager models where exchanges contribute to each other’s liquidity (earning a share of trading fees as affiliates), and similar solutions that improve user experience off chain, while retaining the integrity of a blockchain settlement layer. In doing so, exchanges operating with the 0x protocol should be able to address issues such as poor liquidity and slippage.
One example of a novel solution to the user experience challenges faced by decentralized exchanges, facilitated using 0x, is ERC dEX’s Aqueduct tool. The primary focus of Aqueduct is creating an operable open-order book solution where users of the  ERC dEX relayer have access to buyers and sellers across other 0x operators. This means a wider pool of options to match orders. This system creates both a wider circle, and also creates incentives for users to add to this circle.
Another major aspect of the Aqueduct solution will be the addition of API layers that will help users access detailed, granular information on trade history, order data, and other potentially useful information.  
Conclusion
Decentralized exchanges may win over their centralized counterparts when it comes to security (arguably, some may contest), and alignment with the fundamental crypto philosophy of ‘decentralization’. However, when it comes to other relevant metrics such as liquidity, user experience, trading pair options and accessibility, centralized exchanges currently offer far superior options over DEXs.
It is not surprising, therefore, to see such a continued divergence in trading volumes between the two trading platform choices. NonETHeless, DEXs are a crypto infrastructure solution with considerable potential, and their usage could accelerate under the right market circumstances. Certainly, the smart money sees the potential for the technology — as evidenced by events such as the Coinbase purchase of Paradex.