So what I’m wondering about is how research positions in government run research labs with organisations like Australia’s CSIRO or America’s FFRDC labs compare with equivalent positions in academia and industry.
I work for a US Government Research Agency, so here is an answer based upon my experience (i.e., n = 1):
What are their pay and conditions like, relatively speaking?
In this US, some labs are run by contractors (e.g., some DOE labs like Sandia). Others are run by the federal government (e.g., other DOE labs). I am an employee of the US federal government. OPM describes our benefits (link here) and the GS pay scale is here for 2019. Most research scientists are between a GS-11 and G-15, which a post doc starting as a GS-11 or 12 depending upon the agency. Some federal scientist become Senior Positions (ST), which are above the GS pay scale (OPM page here).
Most research positions in the US Government are "Research Grade Evaluation" (link here, which means we have a review ever 4 years (similar to tenure), where the panel of our peers can recommend our we say in the same pay grade, be promoted, or demoted a level. Some agencies like NOAA and DOD have switched to pay bands rather than the GS pay scale.
How much job security do you have?
Probably similar to a US public academia setting. But, rather than be subject to the whims of state-level politics (US public universities), we are subject to federal politics.
How much control do you get over your topic of research?
This depends upon the position. I am free to study anything falling within the mission area of my agency and my local center, as long as I obtain funding for it through internal or external funding mechanisms. This is less than an academic in theory, but in practice, if you like the applied science of your agency, this is enough freedom for many people including me. Plus, I like directly working with managers to see my research applied.
Here is a link to an obligatory PhD Comic on Intellectual Freedom.
Last, as another answer noted, your questions are largely specific to a given organization. I suggest researching different agencies you might like to work for and reaching out to researchers at those agencies to conduct information interviews. During those interviews, ask similar questions to the ones you posed here.