It seems like every week there is a new option for storing and organizing photos. Just to name a few there is Flickr, Apple iCloud Photo Library, Google Photos, and Dropbox. Roughly speaking these can be divided into two categories free and not free. Flickr (owned by Yahoo) and Google are free (with some restrictions). Apple and Dropbox give you a small amount of free storage and then charge for space.
Flickr and Google also have more built-in features for managing your photos. You can read a good comparison here. A few highlights: Google offers unlimited storage but has a limit of 16MB per picture and they compress your images. This is bad news if Google Photos is your only storage medium for photos. The compression is not lossless (Anyone watch the HBO show Silicon Valley?) which means that you loss some of the fidelity of your image. This is not a big deal for viewing on the computer or for small prints. But if you want larger prints at some point this is a big deal.
Flickr has a total storage limit of 1TB but stores your photos in their original format with no loss of data.
Another thing to be concerned about is the license agreement for these services. Normally we all just check Agree when the paragraphs of legalese pops up for us to approve. However, if you are concerned about your privacy and ownership you should pay attention. Some of these services (Google) claim the right to use your photos anyway they choose. Further, Google has and continues to develop very sophisticated recognition software. You may upload your latest vacation pics from Hawaii and then notice Google displaying ads about Hawaiian real estate for sale or vacation deals. Or they may notice who you spend time with, where you eat dinner, etc.
Apple has two ways of managing your photos: iCloud Photo Sharing and iCloud Photo Library. With Photo Sharing all the pictures you take with your iPhone are shared to all your other devices. Every device will have its own copy of each photo, and every device will have it’s own organization of photos.
iCloud Photo Library works differently. All photos will be sent to iCloud and will not reside on any device. iCloud will be your central repository for all your photos and they will be accessible from any of your devices. This has two advantages: 1) All your photos are safely backup up in one location, and 2) You only need to organize your photos once.
What the Apple iCloud Photo Library service has going for it is seamless integration with the entire Apple ecosystem. So if you have MacBooks, iPhones and iPads and use Photos to organize and view you pics then the Apple iCloud service is the easiest way to go but you will pay for storage.
As for privacy, to my best understanding, and at least for now, Apple says that as long as you keep your pictures private it will not do anything with them.
Dropbox, where you also pay for storage after using your free allotment, has the advantage of sharing. Apple allows you to share albums but the Dropbox sharing is great for collaboration like if you hire an organizer to help you with your thousands of photos.
Bottom line, there is no right answer here, just lots of options with trade offs.