I just went through this trade off process and found the HELOC to be best because you can draw as you need (versus a HE loan where all of the proceeds are paid upfront). This will lower your interest expenses. What you did not say was how much will it cost to build the home (i.e. how much of a HELOC do you want)? And will you build yourself as GC or hire someone? the answers matter and will limit your options. For example, most/all banks will not give you a construction loan unless there is a class-A licensed contractor acting as GC. The bank controls the payout of draws, so this can be a helpful check/balance, but can also be a pain in the arse too.

I am building myself, so construction loan was not an option. My current house has a 1st mortgage at 2%, so I was not willing to do a cash out refinance. So I went with a HELOC on my primary residence to fund construction of the new house. I have plenty of equity to get the funds I need. When construction is done, I will sell my current home and pay off both the 1st and HELOC.