I'm a developer and looked into this issue. There is no new drag and drop API for apps to support, but there is a new type of thing that can be drag and dropped.
Basically, whenever you drag an image in Os X, it tells the target app something like "Dragging an image! Can you handle this?", and then the app says "yeah sure, you can put an image here!". This is how it works in iPhoto and almost every other app when you drag an image. However, it's different in Photos. Basically, when you dragging a photo from Photos, Os X says: "There will be an image in this location for you at some future time. You should load it once it's there. Can you deal with this?" The thing that is dragged is not of type image, but a promise of an image in the future. Very few apps can deal with this - not even Apple's very own image drag and drop sample application!
I have some suspicion why Apple changed this behaviour: with Photos, it's possible that pictures aren't available locally and only stored in iCloud. Additionally, when dragging photos from Photos, some export logic is done that needs some time (eg., pictures are exported to jpg, even if the original is something else). So Photos needs time to prepare before the photos are ready for the other app. That's why Photos can't hand over photos directly when doing drag and drop.
Apple could change this, and allow "normal" drag and drop of pictures with that are available offline. But this has disadvantages: Drag and drop would, seemingly randomly, not work if pictures are not available offline. Drag and drop would also not work, again seemingly randomly, if you have images in a format that the drop destination does not work with (heic and raw formats come to mind).
On the other hand, it's a problem that it's pretty much only the Photos app that doesn't "just work". From a developer perspective, you have to add functionality specifically to enable drag and drop from Photos.
One possible solution (if anyone at Apple is reading this): When dragging photos, Photos could indicate via some progress ring next to the images that the images are being prepared. Normally, this should be fast. Once the ring is complete, photos can be drag and dropped in the normal way.