What do you like best?
When you build an FME tool, you can set it to run on a spatial database while Arcmap is still open, and the tool will not lock! As if that's not enough, FME is continually adding new transformers to their toolbox. When you want to learn a new FME skill, all the training and chat support is free. They offer beginner training as well as advanced training on FME Server.
What do you dislike?
FME has a lot of transformers, and the names are not the same as Arc Toolbox. For the beginner, you have to get used to this. The good thing is, FME chat is free. You can tell the chat box what you are trying to achieve, and the FME support specialist will give you some ideas. Sometimes you have to request a few times before finding the transformer that works best for your task. The transformers work differently tan Arc Toolbox tools, so you have to think about solving your problem from an FME perspective, not an Arc Toolbox perspective.
Recommendations to others considering the product
FME is a great addition to your toolbox, but not a replacement for ArcMap. It has a graphical interface, similar to ArcToolbox. There is free, instructor-led training available online, from beginner, to advanced to server. The training includes access to remote desktop computers, and the manual.
What business problems are you solving with the product? What benefits have you realized?
I use FME to analyze and manipulate data from pipeline databases, particularly PODS relational and spatial. For repetitive tasks, I put these new tools on the FME server.