WP All Import Pro, also known as WordPress XML and CSV Import plugin, is the most complete and feature-rich import plugin for WordPress and Woocommerce. It even has support for Advanced Custom Fields plugin which allows it to import custom fields too. It has the option to import data into existing data. It can even import images to your own server without any problem or connection breakage.
This is the EXACT same plugin as distributed by the developer on WP All Import. The developers’ links are provided above.