What do you like best?
Disclaimer: Our University utilizes Box, so we don't pay a subscription fee. That being said, it's price for 1tb of storage is better than Dropbox's, so I would most likely choose Box over Dropbox for a paid subscription.
That aside, I do really like this product. It works seamlessly on my computer to my phone, and it makes editing files on the go easy with the Office suite. I also enjoy that I can send links with permissions to people outside the organization, so I don't have to invite them to an entire folder.
I also really enjoy the ability to have roles inside each of the box folders that are being shared.
What do you dislike?
Syncing can sometimes be an issue, and when it comes to Mac/PC, filenames can be a bit tricky. We have to make sure that we're using consistent characters that the PC accepts for filenames. Other than that, I really don't have a lot of issues with this product.
Recommendations to others considering the product
Another feature of box that is really helpful is being able to assign roles inside the boxes you're sharing. This helps when you have different levels of users who are sharing the same box. Also it's plans are reasonably priced.
What business problems are you solving with the product? What benefits have you realized?
We are able to have one place where each of our department keeps files that we need to share. It has helped us several times when we've had a machine crash as all the files are in the cloud as opposed to on a hard drive. We use it for sharing files with outside companies as well, and find that it has a few less clicks for those users than Dropbox did, which makes it easier for those we share with.