In Texas, a lot. On first blush, it would appear that the tort of interference with a business relationship (sometimes also called a "prospective business relationship") would be the more potent tort because it would cover more situations. Where a contract exists, a business relationship must surely exist, while some business relationships may not involve existing contracts. However, the tort of interference with a contract is actually the more potent of the two because of the nature of the conduct required to make each tort actionable.
In Walmart Stores, Inc. v. Sturges, 52 S.W. 3d 711 (Tex. 2001), the supreme court held that, in order to be actionable as interference of a business relationship, the interfering conduct itself had to be tortious or otherwise unlawful. Otherwise lawful conduct cannot form the basis for interference with a business or prospective business relationship. This holding makes that tort much less potent because, if independently actionable conduct were committed by the defendant, one already has a basis for liability, and the interference claim would be nothing more than icing on the cake in most circumstances. One circumstance where it might be more than that would be if the damages flowing from the interference were greater than those flowing from whatever tortious conduct was involved in committing the interference.
On the other hand, the conduct that can constitute tortious interference with a contract can be completely legal. The Court gave an example where A was under contract to perform a particular service to B; and C, knowing this, simply induced A to breach his contract with B by offering him a better deal. Offering A a better deal is not of itself illegal or actionable.
Thus, where there is a contract, this is a tort which is much easier to prove. If a contract exists and the defendant knows it, any induced breach causing damages will be actionable. cf., ACS, Invs. Inc., v. McLaughlin, 943 S.W. 2d 426, 430 (Tex. 1997). And this will be true even if the inducement was otherwise legal. Wal-Mart Stores, supra, at 716, 717.