What do you like best?
I like that Flow is an opinionated PHP framework, that guides you to becoming a better programmer and enforces common coding standards across the team.
It has a strong focus on Domain Driven Design, allows for some fancy Aspect Oriented Programming patterns (but please don't overdo it!) and it seats on top of Doctrine and some Symfony components, making them a bit more opinionated.
Flow also has a nice CLI interface for running commands and generating boilerplate code.
What do you dislike?
You have got to keep an eye on performance, and know how to optimize it. Sometimes its strong side, the opinionatedness, may become its weakness, when you want to use it for some highly specific project use-cases.
Recommendations to others considering the product
Check out their support forum at http://discuss.neos.io and Slack channel at http://slack.neos.io. Flow has an incredible community behind it, so don't neglect it!
What business problems are you solving with the product? What benefits have you realized?
We are mostly using Flow to write plugins for Neos, the CMS that is built on top of it. It gives a lot of freedom in creating web sites and web applications, compared to similar CMSes, but staying on budget compared to heavy unopinionated frameworks like Symfony.
Sometimes we use it to write simple CRUD apps on top of Doctrine, and it saves a lot of time of not needing to configure it by hand. Convention over configuration really speeds initial development time!