They have a similar end result on wages, maybe. It doesn't matter if your paycheck (and public benefits) decrease outright because of austerity or its silently

They have a similar end result on wages, maybe. It doesn't matter if your paycheck (and public benefits) decrease outright because of austerity or its silently inflated away. They differ though on who pays overall. Inflation is a tax on anyone holding €-denominated assets. For those who have denominated debts at a fixed interest rate, it's a boon. I'm sure France wouldn't complain if they end up repaying their 10-year bonds at a negative real return. Austerity is largely the opposite: countries (and people) who are in the worst financial situation feel the most pain. It's perfectly understandable that those with money will want more austerity, while those without want more inflation.