Setting aside the technical detail (gold vs. silver), the debate was really over hard vs. soft money. The issue is as relevant today as it was in the 1800s.
Hard (scarce, gold) money policies favor lenders, who care very much about getting the full real value of their loans back. Inflation eats into their returns by decreasing the future value of money.
Soft money policies favor borrowers, who pay back loans in ever cheaper currency through inflation. Buy a farm today with a 10-year loan, and every year the real value of the money you pay back (factoring inflation) decreases.
What we see with a lot of the interest in Bitcoin is a direct reaction to decades of soft-money policies by the world's governments.
Here's the money quote:
... There are those who believe that, if you will only legislate to make the well-to-do prosperous, their prosperity will leak through on those below. The Democratic idea, however, has been that if you legislate to make the masses prosperous, their prosperity will find its way up through every class which rests upon them. ...
This is what the Cross of Gold speech was about, in a nutshell.