What do you like best?
Fast and easy to get started. I can implement new features and make changes to my existing code base very quickly. Meteor is very opinionated, but because it was built on nodejs, you have the entire catalog of NPM at your fingertips.
Meteor is also incredibly easy to learn.
It's an SPA framework, so it shifts a lot of the computational power away from my server and onto my user's device. This is great because I can spin up a tiny VM and still serve plenty of users.
What do you dislike?
It's too closely tied to mongodb. I could use npm to import other db drivers like postgres, but I would lose a lot of the native support for mongodb that meteor baked in (e.g. minimongo on the client, meteor accounts, etc.).
Some people don't like Blaze (the reactive front-end templating system that comes with Meteor), but I personally love it. Also, meteor does integrate well with angular and react.
It's a bit of a memory hog. An idle server requires 200-300mb of RAM. Furthermore, you need to be careful what you "publish/subscribe". My understanding is that anything you "publish" from your server gets put into RAM, so if you have a lot of users who are subscribing, you'll quickly blow through the memory on your server.
The phonegap integration is great, but it's done some handwaving to achieve the appearance of a native integration. When you run into a problem, you have to learn "the Meteor way of doing things" to fix your problem rather than relying on the plethora of phonegap build solutions you can easily find on stackoverflow.
Recommendations to others considering the product
One additional comment. Meteor is very young (it just released v1.0 roughly a year or so prior to the writing of this review). For that reason, it is constantly changing things. For instance, a few months ago, they announced they were dropping support for Blaze (their reactive templating engine) in favor of react, only to recant a few weeks later after significant community backlash.
Also, they've been promising things like native SQL integration for months but haven't delivered.
It can sometimes be frustrating as a developer for the future of the framework to be developed SOMEWHAT in the dark. I say somewhat because they do have a Trello board and are pretty good at communicating with the community.
What business problems are you solving with the product? What benefits have you realized?
Speed, speed, speed.
Meteor allows me to spin up new features and apps incredibly quickly. It may not be the best choice for a large team of distributed engineers, but for small teams it's incredibly valuable!