As has been posted, you'll have to be more specific. It's often a matter of marketing. AA sells exactly the same cabin as First within the U.S. but as Business on its Caribbean routes, totally for marketing reasons.

As a broad generalization with many exceptions, business class on aircraft that also have a separate First Class cabin tends to be a notch below what's sold as Business Class on aircraft that don't. This applies both within an airline (comparing, say, AA's Paris flights on 757s that offer only Business Class with those on wide-body aircraft that have F as well*) and across airlines (those that don't offer F have generally upgraded their J offerings to compete, such as Delta's "BusinessElite").

From what I've seen, most of the folks in F are there on upgrades, award tickets, non-revenue tickets, two-for-one deals, deep corporate discounts and so on. A few pay the full advertised fare, but that's not what fills the cabin.

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*The J seat is the same in both, but the "soft product" isn't.