I've flown international first and international business, each several times.
The major differences are lie-flat beds in first (although some business classes are installing them, or so I've heard), wider seats, and more legroom.
In a 747, for example, a first-class cabin will be five across, and business class will be seven across. Coach will be 10 across. First class will have enough leg room to put your feet all the way out in front at a 90-degree angle and still not touch the seat in front of you. Business class varies, but it's not THAT spacious.
Meals in business and first are similar, but first's are fancier. But it doesn't really matter, because at that altitude it's very hard to taste. In first, they'll have the very highest-shelf alcohol, but that's no big deal either, because unless you're an alcoholic you won't drink a whole lot up there.
The reason: Altitude makes you metabolize it faster, and you get a hangover within a couple hours. Plus the top-top shelf stuff is wasted on altitude-blurred taste buds.
Beyond the specifics, first class is like sitting in your living room. In business, you're on a comfortable train, but you're still conscious of being in a transpotation conveyance with a bunch of other people. There's a higher staff-to-passenger ratio in first, but service in business is quite adequate.
Bottom line: Even on someone else's dime, I think first is a waste of money. If I win Megabucks, I'd probably still fly business internationally, except maybe for first on a Singapore Airlines A380, which has private cabins in first. That would be interesting, but it's so expensive that it's not even really first class, but a super-first.
The best business class I've been in was Korean Air from Seoul to Seattle a few years ago. The food was great, the service was great, and the seats were very comfortable. Lie-flat first class seats have never worked for me. Too narrow and too hard. I couldn't sleep.