Mathematically they're entirely equivalent. Although I'd be inclined to agree that negative income tax might be the better model, as it gives the most direct c

Mathematically they're entirely equivalent. Although I'd be inclined to agree that negative income tax might be the better model, as it gives the most direct control over the net-income vs gross-income curve, and it's the properties of that curve that drives people's behaviour. For instance the steepness of the curve indicates how much someone is incentivized to earn more (ideally you'd want this to decrease strictly monotonically as people earn more, but somehow this is rather controversial). And its curvature dictates whether a stable or unstable income incurs more tax (this property doesn't seem to be used much but it's still interesting). One of the problems with income dependent welfare is that it messes up the lower end of the curve, making its slope smaller or even negative. In the worst case it provides a financial barrier to people on welfare to re-enter the work force.