This is a difficult topic because there's really no way to make a straight up comparison.
Public sector jobs (Federal, State, County, City), in my experience, are much more highly paid than private (on average).
You can pull up "average" data and say that you aren't comparing apples to apples, that the Fed jobs are harder and require more skill - but is that really true?
I don't know the answer to that because there are literally millions of people all over the country on the Federal rolls, and county and state. I'm quite sure it varies a lot by agency, state, job, etc.
I worked with a lot of Fed employees when I was in the military, and they were top notch. But they were STEM/ high tech. And those friends of mine who stayed in and transitioned are living pretty large right now. Their paycheck is on average a bit higher than the private counterparts. Bennies are much much better. However, I also worked with a lot of administrative staff who were still there because it was really hard to fire people. The only reason we were able to get rid of our secretary was to promote her to be someone else's problem.
Now, I'm a bit of a dinosaur - so to be honest, I don't even know if they HAVE secretaries anymore. Our office of about 20-30 people had 3 to 4. Because we wrote letters. And they got typed up, on actual typewriters (though everyone had a PC within my first year). So I had to have the secretary type my correspondence. I'm guessing that they don't do that anymore.
Same thing goes with our local government. Some of our local folks are top notch. Some of them get their family in (nepotism), some people get arrested for stealing a couple of million dollars. We have sheriffs that retire at 50 with full medical coverage and $150k pensions for the rest of their lives.
So, in some cases, Fed employees are living high on the hog in retirement when they REALLY weren't "underpaid compared to the private sector". (I have a few neighbors who fit that category and DON'T GET IT.)
In some cases, Fed employees (and local govt) really were underpaid, but chose to exchange that for security. And their pensions aren't quite so generous.
Either way, whomever said it's a "race to the bottom" are totally right.