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A 400K mortage [at] 5.5% for 15 years sounds like a good deal. I am assuming that
you do not have that much equity in the house with such a big mortgage, so
getting a 100K HELOC might be a little hard. You also have to consider closing
costs. Plus your existing mortgage interest is tax deductable. I think the
interest on a HELOC has some limitations.
It might be less painful to just stick to what you have now rather than to
start the whole process over again with the HELOC ( application fee, appraisal,
credit checks).
Let's assume you get the HELOC. That means you will have a total of $500,000 in
loans. Are you prepared to handle the monthly payments? You have to weigh all
possibilities and decide which is best.

My bank offers a standard loan, or a line of credit. What's the best
way to finance our home addition?

One year ago we moved into our newly built house with about $400,000
mortgage at 5.5% for 15 years. Our addition will cost $100,000 and the
bank is suggesting a 10 year repayment period.

What is the best way to go?