This week, Sen. Bernie Sanders announced his latest big policy idea in his bid for the Democrats' 2020 presidential nomination: He wants to wipe out all $1.6 trillion of Americans' student debt. Every last cent.

A few weeks ago, Sen. Elizabeth Warren proposed a plan that, while it didn't go that far, is still estimated to eliminate all student debt for 75 percent of the 45 million people who owe it, and reduce at least some of the debt for 95 percent. Others in the Democratic primary have proposed more modest plans, but for sheer scope and ambition, Warren and Sanders are the ones to beat.

How do these two left-wing populists stack up against each other, then?

First, let's deal with what Warren and Sanders both want to do. They aren't just out to fix the current student debt problem; they want to make sure a similar crisis never happens again.

To that end, both of them aim to make two- and four-year public colleges tuition-free for everyone. And their plans for that are pretty similar: Institute a big new federal funding program to cover the money that colleges and universities rake in from tuition and fees now. Both Warren and Sanders have ideas for helping out students with other college related expenses as well. And they want to bulk up funding for historically black colleges and programs like Pell Grants to give minority and low-income students an extra boost.

Not surprisingly, the amount both candidates would spend on this specific goal is roughly the same: between $600 billion and $700 billion over 10 years. They would also face similar challenges. Since most higher education is run at the state level, state governments would have to voluntarily participate in the program for their colleges and universities to get rid of their tuition. The history of ObamaCare's Medicaid expansion — which has still only been accepted by 34 states — suggests that might be tricky. But the basic common-good logic of this sort of program has tended to win out over time.

Where Warren and Sanders really differ is in how far they want to take the debt cancellation itself.

Sanders is straightforward in this regard: He wants to cancel it all. That will require spending another $1.6 trillion, for a total spending package of $2.2 trillion over 10 years.

Warren doesn't want to go that far, so she sets up a more limited debt relief offering, on an income-based sliding scale. All households that make $100,000 or less a year (i.e. most Americans) would get $50,000 of debt wiped out. For households making above that threshold, the debt cancellation would slowly decrease in size until it hit zero at $250,000 a year. Thanks to that means-testing, Warren's debt cancellation plan would only require $640 billion. Which brings her total spending package to around $1.2 trillion.

Now, of those two approaches, which is better?

Well, the argument for Warren's proposal is sort of also the argument against both proposals: In absolute dollars, the majority of student debt is owed by people with pretty high incomes and pretty privileged backgrounds. You can see this just in the spending differences between the two proposals: Warren eliminates the burden for 75 percent of debtors by just spending $640 billion. Covering the other 25 percent requires Sanders to fork over another trillion. A lot of people point out it's not terribly progressive to spend that kind of money on people who are already pretty well off.

Student debt does far more damage to the financial prospects of minority and lower-class students, even though they owe less of it in raw dollars. Right now, the gap in mean wealth for white households versus black households is 12-to-1, and eliminating all student debt would shrink it to 5-to-1. With Warren's plan, then, we'd fix the vast majority of the student debt burden for less privileged Americans, without handing that extra trillion to more privileged Americans.

But there are counter arguments for Sanders' approach.

For one thing, that debt burden on wealthier Americans can still harm people further down the income ladder, by distorting how the former behave in the economy. Higher student debt loads make Americans more risk averse, reducing new business formation. A well-heeled lawyer who owes a ton of student loans might decide to take on high-powered corporate clients to pay off that debt, rather than taking cheaper work representing workers and poorer clients. Lots of doctors who pull in big six-figure salaries also have staggeringly high student debt loads. That probably makes them more politically hostile to other progressive goals like reducing drug prices and passing Medicare-for-All, since those programs will reduce the incomes doctors need to pay off their debt.

More broadly, as well-intentioned as Warren's means-testing is, it can also be corrosive to social and political solidarity. The people who do benefit from the means-testing can be marked as freeloaders, while the people left out curdle in resentment. And that can have consequences in terms of who the two groups vote for. By contrast, universal programs send the message that we're all in this together.

As a friend of mine put it, spending on higher education is like spending on roads or public parks. You're doing it for the health of all society. And sure, if you make it free to everyone, the wealthy benefit more, because they have more money they can then spend elsewhere. But it would be kind of crazy to charge admission to the country's highways or national parks with a sliding scale fee that increases with income. A better solution is progressive taxation on the rich to scale back inequality across the board — something both Warren and Sanders are very much in favor of.

Warren's plan to cancel student debt has more technocratic finesse. But Sanders' plan arguably tells the stronger moral story about what kind of country we should be.