Displayed Spreads on Maker/Taker exchanges are typically narrower than spreads on Taker/Maker or other exchanges.
The reason is simple, participants (assuming they pay the exchange transaction fee or get the exchange rebate) would prefer to post their limit orders on a platform that costs the least. As a result, they display them on an exchange that they can access that has the highest likelihood of execution and the highest rebate.
This is often confused with Payment for Order Flow, which is where a market maker on a given exchange pays an order flow provider or consolidator for sending the order to them. This encourages the Market Maker or Specialist to offer a less competitive price (e.g. matching rather than improving upon the National Best Bid or Offer).
Some retail brokers offer 'flat rate' transaction fees (e.g. $7 per trade) so the customer does not benefit from the rebates (or payment for order flow), whereas other offer other models such as 'cost plus' where the transaction fee is lower, but the customer also pays the exchange fees or receives the rebate.