My answer won’t be 100% unbiased either, but abc’s question and some of Michael comments are a good starting point.
The Plug-in/Desktop products follow a somewhat different philosophy. Enfocus PitStop has a point and click approach. You select an element and you can change it. That is great for last minute corrections. pdfToolbox does not offer that. This illustrator like functionality is further completed with GlobalActions and ActionLists which Michael described and allow apply changes to an entire page or a document. Again in the desktop version pdfToolbox offers that as Switchboard Actions and ProcessPlans. I would argue that building a Process Plan in pdfToolbox is less daunting that an ActionList in PitStop, but that comes down to experience I guess. pdfToolbox can be installed as a standalone and a plug-in to Acrobat, while PitStop is only available as a plug-in.
When it comes to automation, if you have many users on PitStop Pro, PitStop Server seems an obvious choice. In reality we see many mixed environments. pdfTtolbox Server has more deployment options. It runs on Linux and Unix (next to and and Mac), has Cloud licensing options which allow you to auto-scale with your cloud environment. PitStop Server these days is bundled with Switch, which adds some additional file moving automation capabilities in there for the price. However there is a Switch configurator/app for pdfToolbox Server so, budget aside, you can easily combine these as well. Further customer feedback tells us that pdfToolbox Server is more stable in high-volume/peak environments in which PiitStop seems to fall over more easily. I would be curious to get feedback from the community on that.
When it comes to individual features, it has become virtually impossible to compare. As Michael says, both technologies give you more probably more functionality than you require. Best is to reach out to separate resellers/integrators for each of the products, as each has their preference, and get a demo based on your requirements.