Let T be the total amount of money in circulation in a given currency C. When you see a value X in units of C, convert it to C' by X in C' = X / T. There you have it, every currency is already trivially equivalent to Bitcoin in that the supply of C' is fixed at 1.

How they're _not_ equivalent is that the creation of money in existing currencies is centrally controlled. You can get a clearer view of what happens when money is printed by looking at C' rather than C.

For simplicity, pretend there's only the Mint (can create money) and the Public (can't). Initially, Mint has X C and Public has Y C. In C', this is X/(X+Y) C' and Y/(X+Y) C'. Then Mint decides to create Z C. Mint now has (X+Z) / (X+Y+Z) C' and Public has X / (X+Y+Z). The Mint has effectively transferred money away from Public. All arguments against deflation are, basically, Mint will now redistribute the money in such a way as to stimulate the economy.