What do you like best?
With all of ESRI's platforms you have the ability to use all of your data over a wide range of uses. You can start in ArcMap and continue your drawing and editing in ArcGIS Pro, or choose to publish a multi-user map on ArcGIS online. From here you can take your data and make custom applications, or take it to a web page and use it in that demographic as well. With ESRI's current platform the sky's the limit.
What do you dislike?
With ESRI to me it always comes back to bugs that should have been ironed out in beta. They usually get around to fixing the issues, but some of these end up popping back up in later releases over and over again.
Recommendations to others considering the product
Very worth the while to get the whole suite of software. Set up so you can use ArcServer, ArcMap, and ArcGIS Online. Makes your job so much easier.
What business problems are you solving with the product? What benefits have you realized?
ESRI gives me the ability to get my created or downloaded data in the right hands in an easy to use format that all can understand. I can use it to make paper maps for proposals or professional documents, or I can publish a map or webservice for a larger user base.