As far as I know, PB doesn't have any true competition, because PB is a "Knowledge Organizer" (aimed at the personal user). It is not a Personal Information Manager (PIM - ex: Outlook, Franklin Planner), nor a Personal Database (ex: a few million of these programs, mostly in the form of personal wikis these days such as ConnectedText, but there are other products that aren't wiki based, such as Literary Machine) or a Knowledge Capture (ex: OneNote, Evernote, Zoot) tool. It is a tool to point to some knowledge (whether an online resource via an URL or Network location, a shortcut on your machine to a tool or document, or an internal document). PersonalBrain is the card catalog to your personal knowledge library.
There are other tools that can do that for you--- with a little adjustment to how you use those tools. However, Personal Brain does it natively (by its design and user interface). Its usefulness isn't just that it holds all the directions to your various individual bits of knowledge or knowledge databases--- it's that it allows you to easily structure and organize that information in a vast number of ways--- and it also allows you to easily RE-organize that information.
Could it be better? Most definately. For the money charged for the Professional license, there is certainly a lack of basic UI features (the missing keyboard access, mass thought manipulations, very poor and troublesome Notes tool, etc), complete lack of any functional printing capability, lack of some basic information organizing features, etc.
For the money charged for a Core license, I'd find the SAME faults with the UI again--- but I'd let slide several other items outside the UI domain, as PB is quite functional as a knowledge organizing tool. (Could be even better, but that's what Professional should provide.)
For a FREE tool, it provides much more than expected. In fact, there isn't anything to complain about that I can think of, other then they don't allow you to stuff enough info into a thought (ie, attachments), and they don't let you use some different presentations of your data (ie, expanded view).
Notice the problem? It's expectations based on the price. Pricing will naturally generate a base level of "acceptability" of "program roughness" as well as expected features (undo, spell check, Notes that actually save inserted images and don't overwrite the contents of other thoughts related notes, etc) based on other commercial products priced similarly.
I think it should be obvious I love PersonalBrain. But I also understand that if you pop out a chunk of change, as a customer you have a certain level of expectations for features and usability, and PB doesn't meet up to most other apps in similar price ranges for those same elements (mostly in the USER INTERFACE, but there are other items).