Back in 2004, I joined Flickr. Here is the first picture I posted there, taken a year earlier.
It is hard to imagine now, but back then, there wasn't another place where you could post photos and share them with friends, who could then comment on them. A community based around photos. It was magical and maybe a bit ahead of its time.
Flickr got bought by Yahoo! and then failed to keep up when iPhone came around. At first they didn't have a mobile app at all, then they had one and it sucked. Then they improved it and gave everyone unlimited* free storage, but it was too late. Flickr is definitely not dead, but 1) it's now owned by Verizon and 2) none of my friends are on it anymore, so I'm looking for other places to store my photos. Not just the ones I take now, but every photo I have taken since 1985 (which I am pretty sure is the year I took my first photo).
I don't want to manage my photos offline, because it's just too much work to do well: setting up software, hardware, backup. Moreover, online storage offer so much more than one single computer could do well: object / face recognition and fast, smart search are some that come to mind.
Another early Flickr photo, taken with my Nokia 6600
I am an Apple / Mac user so using Apple's iCloud storage and Photo software comes to mind. Their storage is now competitively priced at $10/mo for 2TB that you can even share with family. A great deal that other cloud storage providers can't match yet. However, iCloud doesn't work well or at all on other platforms like Android and Windows, and if Android ever gets awesome I'm stuck. I've been through too many platform transitions to not consider that a deal breaker. (Where are all my Amiga SoundTracker compositions?) Also, most of the 'smart' functions are performed on the Apple-only desktop and mobile apps. This leads to super weird things like having to redo face recognition on each new device you connect to your photo library, and different search results depending on which device you happen to be on. 👎
Dropbox is another option. I have been a happy user of their cloud storage for years, and even though the $100/year for 1TB is not as good a deal as iCloud, it offers great OS and photo upload / sync integration across platforms, including even Ubuntu. They had a dedicated Photos app for a while, but it wasn't great at what it needed to do, and they killed it. What is left is very good automation of photo sync and upload, and a decent photo browser, but no other photo specific features like object recognition or search features.
Then there's Google Photos. It has come a long, long way from back when it was Picasa. It does unique(ly creepy) things like matching photos that don't have GPS tags with places you've been according to your Google location history. If you're uncomfortable sharing lots of data with Google, you're never going to like it and the buck stops there. I have always liked the tradeoff Google offers between stuff they give you, and personal data they ask as currency. What Google does best is search, and that shines through in Google Photos as well. I can search for locations, object types (I have lots of train pictures, see below), people, dates. It all just (mostly) works.
This being Google, there is not really a desktop application. Searching, browsing, organizing all happens on the web. The upside of this is that it's completely portable, and Google Photos works just as well on Firefox and Safari as it does in Chrome. The excellent mobile apps (for iOS and Android) do bring the search functions to your mobile devices, and also take care of automatic uploading. Photo editing features are pretty basic compared to Apple Photos.
So where does this leave me? Dropbox is out for the lack of photo specific features, although I still use it as my secondary backup for everything. Having used both Google and Apple Photos for a while, it really comes down to two decisive arguments: the vendor lock in that comes with using Apple Photos, and Google's super smart search. So my money goes to Google. I just wish their cloud storage would get a little cheaper to follow Apple's lead.