I could tell almost the opposite story about my current position.
The initial offer they made me was an almost 10% pay cut from the job I was leaving. I was able negotiate an offer higher than their initial, but still about 5% below what I was currently making on paper.
There were a few deciding factors, though.
First of all, the insurance employee contribution was about half what I was currently making, and copays were similar to or in some cases less than the insurance I had at the time(for the first several years at my current employer, I had $0 copays on all but one of my medications-that was a big deal).
Second, they actually had a really good, well funded state retirement system that was in place before social security. The combination of it being an older system that provided better benefits to retirees from social security meant that this employer was exempt from social security and I’d not have that taken out of my check(and my per-paycheck retirement contribution is lower that what I previously played for social security+mandatory 401K match).
Third, I was told that due to the way things were structured, extra pay stipends were normal and although not guaranteed, I could reasonably expect them.
What sealed the deal for me, though, was that the union negotiated raises several years at a time, and I knew what the COLs would be for the next several years(and our last few since then have been even better). Further, there were clearly defined timelines for promotions, the requirements for those, and the raises that would come with those.
All of that put together meant that my immediate starting take-home pay was within a few dollars of what I was making, and within a few months of starting one of those extra pay stipends kicked in to give me about a 3% lift over take-home at my previous job.
Even better, though, I’ve been able to secure one promotion(with two additional available down the road). Between COL and promotion, I’m about to see an almost 20% raise this year in base pay. My gross pay last year was about 40% higher than my best year at my previous employer, and this year is on track to be about 60% higher. Meanwhile, my previous employer has given a single 3% COL in the 5 years since I left, and I had almost no opportunity for promotion there. So, that small short term loss has paid big since.