Classical Liberalists think that every man or women is responsible for their own destiny, and that the government should not hinder the individuals, or businesses pursuit of it. They also have no mandate to correct the results of this, regardless of how positive, or negative. They think that people should not be governed differently based on how successful they are. Economic discrimination is a two way street, and wealthy individuals should not lose excess income, or opportunity.
This is why they want a flat tax, similar to GST, to replace the progressive income tax we have now. Reform liberalists believe that low-income individuals will spend a greater proportion of their income on necessities, rather than luxury goods. Therefore they should be subject to lower income tax rates. A progressive income tax is ideal for a Reform Liberalist, as the increased tax revenue from the higher earners will be redistributed to social programs that provide welfare and equality of opportunity for the poor.
A Reform Liberalist would have a problem with the big national oligopolies, as the limited competition restricts consumer freedom, and can lead to the consumers being exploited. Many Classical liberalists would say that there are many large incalculable benefits that these large companies bring, and that they should not be subject to coercive redistribution. This action would violate their Equality of Right, which means the property of each will be equally protected.
The Classical Liberalist, would oppose any regulation on the economy. As they believe that those who are able to make money based on the principle of supply and demand already have helped the welfare of other in the process. Classical Liberalists understand inequality as an inevitable result of free competition, and actually see it as beneficial in the long run as capital is reinvested, to create new technology, employment and opportunities. If this capital were to be taxed heavily instead, many opportunities and jobs would be lost further adding to the inequality of wealth and opportunity for the poor.
The biggest differences between the sets of ideologies is that Reform Liberalism believes in equality of opportunity, and that it is ethical to reduce the freedom for some if it means increasing it for others. Classical Liberalists believe that the invisible hand will regulate the economy and that any wealth redistribution to the poor would harm them in the long run. They believe that everyone should be completely in control of their own destiny. I think that Classical Liberalism is the superior theory as it sticks to very simple principles, and it hold everyone responsible for their actions.