How does EVA improve our knowledge of performance over ROI, ROE, or EPS?

EVA, or "economic value added," is a measure of the value a company has added to itself by investing in capital expenditures and similar things. It is calculated by subtracting the cost of capital from operating profit and adjusting for taxes. In doing this, the company gets a sense of how much its revenue is increasing based on the capital it puts into equipment and other expenses.
This is beneficial for understanding ROI because it gives a financial measure for the economic benefit of every dollar spent on capital expenditures, machinery upgrades, and similar costs. ROI is "return on investment," and to understand it, you need to understand how much money you receive for every dollar you invest. If EVA is negative, it means that you are not earning extra revenue for capital expenditures; if it's positive, you can see that you are earning more, which correlates to a higher ROI.