I believe the difference in these two methods is small but is one method going to always give you more in finance charges? Does it matter as to when and how often advances are made?

These both refer to the balance in the account. It should not impact the APR from a loan, and the APY if tiering or minimum balances are used.

Regulation DD
Sec. 230.2 Definitions.
For purposes of this part, the following definitions apply:
Average daily balance method means the application of a periodic rate to the average daily balance in the account for the period. The average daily balance is determined by adding the full amount of principal in the account for each day of the period and dividing that figure by the number of days in the period.

Daily balance method means the application of a daily periodic rate to the full amount of principal in the account each day.

What method will give you more in finance charges?

It would depend on how the account is structures, when the interest rate changes, what the daily balances are in the account on any given day, and whether your system can even handle an "average daily" balance on a loan account, and whether it is legal under State law.

Our system does handle both. We are looking at merging two banks - one uses avg daily and the other daily bal. Management is looking at the method that will produce the most revenue. When I run a few scenarios I do not get much of a difference - only pennies. Most of the time daily bal is a few pennies more but not always. In the examples the interest rate remained constant. Does one method usually produce more in finance charges?

I'm confused - are you referring to loans or deposits? I'm assuming loans since deposits don't produce revenue?

Yes - the loan side - for ready reserve and Personal Lines of Credit - open end credit.

If your interest rates are static and you don't have tier rates based on balances, there is basically no difference between the two calculation methods