Some comments on their theoretical differences here.
I think Mike Sproul and David Glasner would agree on 95% of monetary economic propositions, only disagreeing on how fiat money gets its value. David thinks there are two reasons for fiat money to have value: either people are irrational, or fiat money provides a real service - discharging of taxes. The latter is a chartal description of money. Mike has a "backing theory" of fiat money, which I think is broad enough to include the tax-discharge argument. I like Mike's because it is a more general theory. But I don't think the two are very far apart.
To tell them apart, ask this question. "If the US government ceased accepting Federal Reserve-issued liabilities to settle taxes and, say, required gold instead, would the US dollar lose its value?"
I think David and most chartalists would have to say yes. Without the ability to redeem it for taxes owed, the US dollar would be worthless. I think Mike would say no, because as liabilities of the Fed, even fiat money has some sort of claim on Fed assets, and this is enough to give it value.