I looked into a few different image sharing options a few months ago, and ended up using Flickr for our team photos. The final decision was between Flickr and Google Photos, but I chose Flickr mainly because of its storage plan.
Google Photos
- More polished interface
- Unlimited photos
- Max resolution of 16 megapixels (unless stored in Drive)
- Integrated with Google services
- Built in embedding (not sure what features it has)
If you are already paying for/willing to pay for extra Drive storage space, you can store full resolution photos in this space through Google Photos.
Flickr
- 1 terabyte of storage
- Unlimited resolution
- Interface has improved recently
- Limited embedding options
I was able to overcome the embedding limitations of Flickr using
nanoGallery (also supports Google Photos). It is entirely clientside, which was good for us because we don't have access to the server code.
This is an example of it in use on our website (it needs better styling, I know).
Flickr and Google Photos are not the only options, but they are the ones I know the most about.
I hope this helps.