IIRC, you cannot deduct the interest on any part of a loan balance that exceeds $100k more than what you originally purchased the property for. Otherwise, both loans have identical tax advantages.
The key differences between the 2 are that the HELOC operates somewhat like a credit card on your home, with a revolving balance that you can borrow against as you pay it down and payments based upon what you owe. Unfortunately, HELOC's also have adjustable rates indexed to the Prime, which the Fed has raised 5 times in the last 7 months, and is expected to raise at least 3 more times this year. HELOCs are only available in one term, 20 years, with an initial draw period for the first 10 years. The traditional loan is usually available with a fixed rate and term (with a variety of terms), so that you know the payment and interest rate will never change, but its disadvantages are that the initial interest rate will be higher than the HELOC, and that you will never have the option of making a lower payment as the balance goes down, nor of being able to borrow against it again in the future without refinancing.
Whether you get a HELOC or a traditional 2nd mortgage, the actual interest rate and product available to you will vary greatly depending on your credit score and LTV (how much you borrow against the value of the property).
edit: you're right, Mill. Those 125% loans are not tax-deductible. Yet one more reason why I am so against them.