That is very personal call and it really depends. I had an offer from a major automotive studio in the LA area, pretty much a dream job for me. But the pay I was making as a senior designer for the company I was working for in Portland was already more than their creative director was making. After a lot of thought I didn’t take it, and I think it worked out for the best, but in that case I was already working at a dream job. If I was working in an industry I didn’t like at all I think I would have personally jumped for it, but I don’t have kids and my wife is pretty flexible with moving around (within reason, as long as it is a place she wants to be too.)
When I went to frog it was a pay bump, but SF was so expensive, it was still in essence a cut. But my wife and I made the calculated decision to go for that one. One of my mentors had the opportunity to be creative director for one of the most famous furniture companies in the world, and he is a huge furniture buff. He ended up not taking it, but is now VP of design at the company we worked together at and is super happy… and is on the board of directors at that furniture company now…
Short answer, there is no right answer. Sometimes you have to make a decision and then make it right.