First, remember that the terms "First" and "Business" class can mean very different things.

Coach is pretty much coach, a narrow cramped seat with bad food on international routes and no food on domestic.

Domestic first is a wider seat with slightly more legroom, free drinks, snacks on shorter flights and something resembling food on longer ones, a tolerable experience.

Some transcontinental first routes in the USA have upgraded first class, with much larger seats, better food, sometimes almost as good as international business class.

International business class is sleeper seats, sometimes lie-flat and sometimes almost lie-flat, tolerable to sleep but a bit narrow, pretty good food relative to what can be served on an airplane, blanket, pillows, noise-cancelling headphones, a very nice experience if you're awake and decent if you can sleep. Also incudes lounge access in airports.

International first class is always lie-flat seats, wider, very attentive service, more privacy, often a desk-like unit. The quality of the product varies widely, with some airlines trying very hard to do anything "over the top" that they can. All the Dom Perignon you can drink? No problem! Some airlines also have first-class lounges that are an experience in themselves, people have been known to try to fly Lufthansa through Frankfurt just to use the lounge. Ever been driven to your plane in a Porsche? One of the icons is the rubber ducks in the showers in the first-class lounge, if you're going to fly F on Lufthansa, you have to get one for a souvenir, even if you don't need a shower!

So that's the quality difference. Now you have to factor in the price difference in miles, and sometimes in fees. Most people on this board would agree that the relatively modest difference in miles between coach and business class on international flights is worth it. I've only traveled overseas once, it was in business, and I think if I had to fly coach I'd stay home. I wouldn't even think of paying double the miles for F on a short domestic flight. If I were going transcontinental, even if it wasn't one of the upgraded transcons, I might go F, but I'm getting very cranky about flying coach and right now I have a lot of miles. On the other hand, if I could fly on an airline I have high status on, I might just buy a coach ticket and hope for an upgrade and settle for coach if need be. I can say that when I travel with my wife (which isn't that often) I find the trips are a LOT more romantic in first/biz than in coach, but if we're just flying an hour or two I don't worry about it.

Another good point was made that in particular on Delta, you often have to pay 40K miles for coach, so clearly 45K for first is worth it.

There's another way of looking at what you "pay" for first. I just started a new job where I will be commuting between the east coast and Bermuda. I bought gold status on USAir so that I could check lots of bags and take my stuff to Bermuda for free, but to keep the status I have to fly lots of segments. On the way out I can leave at 7AM and fly to Philly, or leave at 5:30AM and fly to Charlotte and then Philly. On the way back, after getting to Philly I can fly home immediately and get there at 8, or take an extra hop or two and get home at 11. So in my case, to get the extra segments to keep my status and get upgrades I am paying not in dollars but in time. As said before, I'm cranky about flying in coach, and there aren't that many elites flying PHL-BDA (mostly insurance and finance guys like me who work in BDA and still have families in the USA) so it's worth it to me to take these extra flights to make sure I get more of a shot at sitting up front.