why would a reduction in welfare benefits for the poor and a tax increase for the rich have different effects?

Question

Why would this reduction in benefits and increase in taxes have different efects on work effort?

Answer 1

Reducing welfare benefits causes the consumer to buy LESS. Therefore reducing the demand for goods & services.

A tax increase for the rich is just the opposite.
Large corporations counter tax increases with tax deductions.
A few of these deductions are:
Employee wages and most employee benefits
Rent or lease payments
Interest on business loans
Real estate taxes on business property
State, local and foreign income taxes assessed to your business
Business insurance
Advertising and promotion costs
Employee education and training
Education to maintain or improve your own required business skills
Legal and professional fees
Utilities
Telephone costs
Office repairs

Answer 2

Both tax increases and reduction of welfare benefits would reduce demand. If the welfare beneficiaries are able to work it would also increase the supply of Labor and put downward pressure on wages.
A tax increase would act like a wage cut, and would decrease the supply of labor, (for people not on the back bending part of the labor supply curve) and put upward pressure on wages. I don't see any reason the the rich would respond differently to a tax cut than ordinary people unless you are assuming progressive marginal tax rates or that they are more likely to be on the backward bending labor supply curve.