They don't make intellectual disputes like this one anymore. These days, a "dispute" means that two academics make a few long-winded criticisms of each other's ideas in obscure journals and then wish each other well.
The Descartes-Voetius War, which lasted more than 10 years, started a bit like that. Voetius, a Dutch Calvinist theologian, criticized Descartes's thought for being opposed to Scholasticism as well as for having negative theological consequences. Okay, that's standard stuff. But then Voetius upped the ante: he said Cartesian philosophy could no longer be taught at the University of Utrecht (the ban was in place for 363 years [source]). That's getting a little worse.
After that, Descartes published a defense of his ideas, with maybe just a few little attacks against Voetius's character and intelligence thrown in. Uh-oh: this time it's personal. Voetius got angrier and angrier. It wasn't enough just to accuse Descartes of being an atheist (though he did that). He also claimed that Descartes was libeling him, after which he threatened Descartes with arrest and almost had his books publically burned.
Descartes was terrified. He even sought the protection of the French ambassador. When that didn't work, he finally issued a public apology to Voetius. (Not his finest moment, as he would agree.) Shortly afterwards, Descartes left the Netherlands for Sweden. Where he died.