You should put the money where you can get the highest return. Paying off the debt is an effective 3% return since you are eliminating the interest payments. My guess is your savings account is earning less.
However, investing the funds in low cost stock/bond funds/ETF's should, on average, provide > 3% over time. My suggestion is to keep enough emergency funds in your savings account and then invest any excess above that. Also, reduce the debt payments to the regular payment (not 4x) and take the extra 3x and invest that as well.
If the debt you had was at a higher interest rate, say 7%, then I would suggest paying down the debt first since most people are suggesting using a 5%-6% long term average for stock market returns for retirement planning. But, since it is at 3%, investing should take priority.