The difference on my most recent test was about 10%. Also note that some small establishments might give you a better cash price. You might also find it easier to get a ride (Cabify, Uber, etc.) if you choose the Cash payment option. You may also find that you can only leave gratuities in cash. Also, just because you believe the currency is "utterly worthless," and most residents of Argentina think the same, it is their currency, and for those other than those with real means (i.e., not the service people you'll generally be dealing with), it is their reality of life, and I politely recommend that you not engage discussion on the topic other than with friends and/or family during your visit.

If you end up with a small stack of bills when you get to the airport to leave the country (I assume you'll be flying out), you can always buy something at the Duty Free shop and top the purchase off with a credit card.