When it comes to water quality, you goal should be stability. When you do monthly water changes, you are allowing for greater swings in your water parameters. Your Nitrates may climb to 30 over the course of the month. Then when you do your water change, they may drop to 10. So over the course of 1 month, you are getting 20 point swings in Nitrates.
When doing the water changes weekly, those swings may only be 5 points.
My preference would be to have Nitrates sit consistently at 30 than to have 20 point swings.