What do you like best?
There is an integrated desktop client with options for pretty much any function in the system. Offline transactions saved our butts a couple of times when our remote site lost network connectivity. It was easy to upload and reconcile the offline transactions. The addition of the Web Services API's made life a lot easier for us and they seemed to work pretty well.
What do you dislike?
The client, while integrated and near feature complete, is definitely a design of the past. It would be nice to see a proper web-based client (one that does not require purchase of a cloud solution). The public catalog option was abysmal, which is why we opted to use an open source discovery layer and require access to Symphony's Web Services API's. The mobile circulation option was almost unusable. We hoped to use its collection weeding functionality, but we couldn't get it to work. The company, while trying to address the drawbacks of their current system, seems to offer promises but ultimately fail at delivering on those promises within a reasonable amount of time.
Recommendations to others considering the product
I'd probably opt to use their cloud-based option for new deployments to save on cost and on-site expertise.
What business problems are you solving with the product? What benefits have you realized?
As an academic library which shares a catalog with a public library, the Symphony system was chosen to fulfill a variety of needs. We needed well-formed support for both Dewey and Library of Congress classification systems as well as intuitive patron-driven search and browse options. We also required both the acquisitions and cataloging modules as part of what we considered to be key to any Integrated Library System. For those purposes, the product works well (with some minor usability issues).