The only difference I can see is that we would no longer control our own interest rates. The Euro rate is currently lower.
I believe that if it is necessary to take money out of the economy, the straightforward way to do it is to increase income tax rather than interest rates. People would not like this, of course, but it is actually fairer. Income tax is paid in proportion to income, whereas increases in interest rates bear down disproportionately on younger people with large mortgages and (often) no great amount of surplus income.
It would require a slight change of mindset, but it would be worth it. The extra income tax could be used to reduce government borrowing, thus also bearing down on inflation. And any rise would, of course, be temporary, until inflation fell.