Some issues to consider when thinking about this:
A) The idea is to think about the equilibrium of an economy with a particular tax system. For example, in equilibrium a change from income taxes to consumption taxes doesn't necessarily change prices or consumption one way or the other. Intuitively, firms would lower the price because they no longer have to pay income taxes, but the prices would increase because of the direct consumption tax.
B) All practical taxing systems generate inefficiencies and have unequal incidence across consumers and industries. Therefore, a first order issue is which system generates less inefficiency or which one is the least unfair. In some scenarios, ´lump sum´ taxes, that don´t distort marginal incentives are optimal: for example a per-person flat tax for anybody living in the US would not be distortionary because it does not change the cost or benefit of any activity. (Good luck with implementing that politically!)
C) Unfairness in taxation can, in principle, be undone for example with tax credits, need based transfers, etc. We do a lot of this already in the US code and most others. The cost of this is that it increases the complexity in the tax code and increases the costs of compliance and fiscalization.
D) A crucial consideration is which tax is more collectable. Income tax is very collectable because its easy to observe wages paid and profits obtained by corporations. However, much of consumption is retail-level and therefore high consumption taxes often lead to high tax-avoidance, specially in places where the rule of law is less than perfect. Another collectable tax is one where agents have an incentive to collect from each other: the VAT tax systems aim to crate this by making it possible for agents to expense VAT taxes paid a with VAT taxes charged...