Sorry as a language model AI, I can’t write an exact 15000-word long article due to the limitation of text generation capacities. However, I’ll give a detailed article about the best photo organizing apps for iPhone.

1. Apple Photos: Apple’s built-in Photos app is perfectly suited for all your photo organizing needs. It comes with smart features such as face recognition and object identification, which allows sorting and categorizing photos based on different categories such as people, places, and objects. It offers features like Memories and For You, which automatically create beautiful collections of your best shots. The powerful Search feature helps find exactly what you’re looking for, based on keywords.

2. Google Photos: Google’s photo management app is known for its unlimited storage, smart tagging, and excellent search capabilities. The app automatically backs up and syncs your photos on your device. It can also sort your images into different categories, recognize faces, and even identify locations where the photos were taken.

3. Adobe Lightroom: Lightroom is another incredibly powerful photo organizer. It offers robust cataloging tools, non-destructive editing capacities, and seamless synchronization across devices. For professionals who need to manage a substantial amount of photos, Lightroom’s capability to handle batches of photos provides effective organization and workflow.

4. Slidebox: Slidebox is a photo organizing app that allows you to sort your images with simple swipes. You can quickly delete duplicate or unwanted photos, sort them into albums, and compare similar photos. A unique feature is that it integrates seamlessly with your iPhone’s camera roll and can even handle GIFs.

5. PhotoSync: PhotoSync allows you to transfer, backup, and share photos and videos from your iPhone, iPad, or computer. You can easily move images between devices, services, and even clouds. It’s an easy-to-use, drag and drop interface which makes photo organization a breeze.

6. HashPhotos: This app provides you with a ton of organizing features that sort photos by date, location, type, and tags. HashPhotos can filter your photos to show only videos or burst images, split-screen view for easy comparison of photos, and quick access to your favorite and tagged photos.

7. F-Stop Gallery: F-Stop’s photo organization features include tagging, a smart gallery that recognizes images with similar color schemes, and a pro version with Google Maps integration and password protection for private albums. You can also individually tag your photos for easy access.

8. Flickr: Flickr provides you with up to 1TB of free storage space, and the app has both photo editing and organization tools. Photos automatically sync with your Flickr account, and you can search and tag images for easy organization. Albums and favorite’s features let you group your photos, the way you want.

9. ACDSee Pro: ACDSee Pro app is a potent tool for managing your photos. It includes advanced features such as metadata editing, batch processing, and smart sorting. The photos are neatly arranged in a folder-based structure for easy browsing.

10. Tidy: Tidy works on a gesture-based interface where you can simply swipe up to create new albums and drag and drop to add photos. It’s simple, clean, and user-friendly.

Do remember to choose an app based on the specific needs you have for your photos – whether that’s simply organizing them, enhancing them with filters and effects, or more advanced features like tagging and metadata editing.