What do you like best?
Microsoft Project is a fully-featured project management program that enables you to manage all aspects of your projects, big or small. It's always been my go-to for gnatt chart development (and maintenance).
Microsoft's interface (ribbon) certainly helps provide you with quick and easy access to the most common elements of the program.
Defining precise tasks, connecting them with related tasks and phases is pretty simple.
Reporting is a tremendous asset. There is a lot of customizing you can do to make reports and gnatt charts look very professional.
What do you dislike?
As Project 2013 is fairly complex, there can be a pretty steep learning curve. While there are sufficient training videos out there for self-learners, using this software professionally may require some professional training so you can get the most out of your time using Project.
Recommendations to others considering the product
I'm not quite sure which direction Microsoft Project will take in a world where start ups are offering simple to use tools for things like website creation (think pagecloud), and other project management software (smartsheet, mavenlink, basecamp). What Microsoft does have going for it is its seamless integration with their Office Suite, and it does a very good job at managing projects in the old fashioned Windows way.
Microsoft does not provide personal customer service support like other platforms do, at least in my experience. Quality of Support is primarily driven through community forums, videos and colleague assistance. I think this is something that MS could do better.
Lastly, cost is a big disadvantage for small businesses and start ups. It's almost a non-starter. Especially when there's other options offering small monthly subscriptions (which MS now does) and might dig deeper in collaboration tools, which MS Project fails to do.
What business problems are you solving with the product? What benefits have you realized?
Time and resource management. While it can also help track budgeting, which we use Sage 100 for, we primarily found it useful for keeping track of tasks and reporting the progress to clients. The reporting, as I mentioned earlier, certainly helps provide further value for clients!