What do you like best?
To me, ProTools is more straight forward than other DAWs. It's most likely due to having more experience using it versus other programs. In the last couple years, I updated from 7.4LE to 11 and greatly appreciate the openness to using non Avid interfaces. I also really like how the internal routing architecture works - it just makes sense to me.
As for the GUI, I prefer a darker look, mainly because I record/work in darker rooms more frequently than not. There are other interfaces out there that have a darker look to them, but ProTools still wins me over.
What do you dislike?
Some of the random errors that come up while using the software can be irritating. Once you have it set up properly they don't rear their head often unless it's something like not having a large enough buffer, CPU is out of juice, etc. One annoyance I noticed with PT 11 is that every time you make an adjustment to the playback hardware (buffer size, driver, etc.), the software restarts itself. I don't remember PT 7.4 doing that, however I like how 11 sounds vs. 7.4, so it's something I'll live with. It does reopen the session you were working on. There are some days where I wish it would work, at least on a basic level, without the iLok. I've had a few times where we decided to record randomly, and my iLok was at home.
Recommendations to others considering the product
Try it out first to see if it's something you like. If you decide it's not for you, there are other great options out there.
What business problems are you solving with the product? What benefits have you realized?
I'm solving the problem of being able to record, edit, and mix audio - studio and on location. There was older software I preferred for editing, but it's not supported by the newer operating systems all my audio work is in ProTools now. One large benefit is most other audio techs. I work with use ProTools, so being able to shuffle projects between one another is a breeze. You just have to make sure plugins are compatible and/or used by the other party.