Both are fine, and will import full quality. The difference is that Photos app will import the photos into its internal library and it will auto organize them, while image capture will import your photos to a manually created folder where you can organize them manually.
If you have iCloud, the easiest is to just enable iCloud Photo Library. Your photos will be automatically synced to all your Apple devices via iCloud. Then enable optimize storage on your phone and iOS will automatically adjust the number of photos downloaded to your phone as needed so you can regain some storage space.