You sum it up well. If you just get static text (call stack etc) from your error logger tool, it's of almost no use as it doesn't reveal the state of the app. With modern tools that have replay capability, this changes and the debugging process is so much nicer. :)
Every error tracker I've ever used allows you to send arbitrary data (which could be your entire flux store, for example) and has great documentation on how to start using it.
We also allow you to attach any custom data to the error report. But this doesn't necessarily help you put the web application into the state where it crashes. Demo of custom data:
