What is the purpose of the PhotoStreamsData folder? The folder PhotoStreamsData contains the same photos as the DCIM folder, only with a slightly lower resolution. Why create (almost exact) duplicates? Is it only to save some space on iCloud? Can I safely delete it to free up some space? Would deletion make any difference to the iCloud sync?

(iOS 9.0.2, iPhone 5c)
In general, deleting files that an application stores internally is a bad idea. This goes double for iOS since the presumption that users won't be idly deleting things is more realistic across the user-population of an app. The reasons for not deleting things are:


the app (or the system) has a database for tracking what's placed where. Deleting the file without cleaning up the reference at best means you end up with another file. At worst, you have crashes and slowdowns caused by the app/system having to sanity check all the files it has placed on the storage.
the files will appear again as the app re-does the work you've undone.


The reasons to place files in different spaces allows the system to reclaim storage space in the even that a cached file can be cleared to make way for other content. It also is baked in to how Photos works - when you run low on storage space, the app can be more aggressive about compressing the local cached copy of the photo. One setting won't be appropriate for people with 128 GB of storage and 16 GB of storage not to mention as you fill up your storage with other items over time. Also, I bet Apple is only backing up the files that are "authoritative" and not thumbnail or resampled versions of the iCloud originals. That saves bandwidth if backing up to the cloud and storage space on the backup and time to complete a backup.

So, I'd recommend making other changes like deleting large apps, large video files and let Photos be photos with storing multiple copies of images and multiple resolutions in different places.

Your DCIM folder is where the photos taken on that device live - so use care not to delete the authoritative copy of a file until it's backed up elsewhere.