We currently have a primary mortgage and a HELOC, and have about 15% equity in our home, but have little savings. We are looking to buy our next home. Will it be easier to get a mortgage if we save up any extra money in the bank, or of we use any extra money to pay off the HELOC, giving us more equity but little money in the bank? We have excellent credit.

Strictly from a fiscal standpoint paying down your mortgage balances and thus eliminating interest is a sound stategy.  Of course that is offset if you take the old rule of having 3-6 months expenses in the bank (money market or short term CD) available for emergencies.

I would also apply the additional principal to the loan with the highest interest rate. That could be your 1st mortgage with prime down to 3.25%.

If you have little to no other savings, I would suggest putting the money in the bank.  If you put it on your HELOC, the lender can reduce your line and then you would not be able to access the funds until you sell.