No system is a silo and your web site is no exception. eCommerce systems consolidate data from your own backend systems like your ERP, PLM, PIM, Digital Asset System, or other operational systems, into a unified experience. These are your primary business systems that are required to interface with in order to fully automate your online business.
3RD Party Applications & Extensions
A fully optimized eCommerce business is dependent on your ability to connect niche services such as returns, tax rates, exchange rates and fraud detection to compliment the overall online customer shopping experience. Both Shopify and Magento provide a vast and growing number of options on the open platform marketplaces. Always start with Shopify's App Store, and also the Magento Extensions Store to evaluate against your needs.
Also, there are many external parties like Google, Amazon, Facebook and others that you will install tracking pixels or scripts to publish your data to and provide access to real-time user data, browsing behavior, orders, shipments, product data, imagery, and other catalog information.
A word of caution...
Shopify apps tend to work more often. Everyone is on the same Shopify version to make things easier for app developers, and all applications go through extensive testing and validation for inclusion into the App store. There are exceptions to this, but for tried and true apps like Signifyd, email marketing, customer service, etc., rarely is a developer required and most apps can be activated within minutes and without hassle.
Magento is an open-source code base, with many different versions, and thus the core code can be changed by any developer or a new code release can break a perfectly working part of your site. Hence, if you have customized the Magento core code by any measure, installing or activating a 3rd party extension or app may not be as easy as it seems (or even break your site!). Doing so often requires a developer and/or support from the 3rd party vendor and/or support from Magento to make it work as described. Before purchasing, make sure you inquire if the 3rd party application you are considering is validated to work with YOUR Magento version, and if they have any customers they could refer you to.
For backend integrations to your ERP, check with your ERP provider. Chances are, your ERP provider has integrated with both Magento and Shopify many times before, and likely has the expertise in-house to guide you on what is and is not possible. Some of these integrations are even marketed and sold by ERP companies as "eCommerce connectors", which you may also have to pay extra for. But in most cases, it's worth buying the connector if it is supported and you don't have to build your own.
For other business requirements that go beyond what is available in the marketplace and require custom integrations, Magento and Shopify are comparable in this respect. The Magento API Web Services and the Shopify API are both worth looking into to see if the items listed here meet your minimum requirements for receiving and transmitting a variety of data and data types.