As an early stage startup, we needed to create the first version of our mobile application having in mind the future need of supporting multiple platforms (iOS & Android). We gave Flutter a try and immediately experienced a smooth and easy way to learn a mobile platform (with Dart) that allowed us to very quickly create our mobile app. The more we learn, the more we can leverage the ecosystem of libraries/plugins for Flutter (https://pub.dev/), the more we foresee Flutter as a very good choice for cross platform mobile development. In comparison, Android (Java) and iOS (with Swift) are powerful languages but they both have a steep learning curve. With Flutter we only had to learn one platform and voilà !
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The real question here is not about the technology but rather your real needs and your data. Do you need to manage data that has core concepts and relations ? (such as a family, with parents and children) or do you need to manage a basic collection of similar data (such as blog entries)? PostgreSQL is definitely a relational database for managing entities and their relationships whereas MongoDB (I may be strongly opinionated here ;-) ) is more targeted at managing collection of entities (such as the blog entries). For an e-commerce site (with some products, products categories, user ratings and comments, prices, bundles...) I would go for PostgreSQL as it will support/guide you in creating a structured data set with all your products, organized in categories and with user ratings/comments attached to them. HTH