Which is better, I have no mortgage on my home

Depends on your needs. I prefer a Line of credit that can be used as needed and you only pay interest on the amount used.

Again I prefer neither and own my home free and clear with no chance of losing it if there was something to happen.

But if there is a grave emergency and you have to borrow money without knowing how long you wish to borrow it for, what the interest rates are and other details it is hard to say.

You have to shop around and find out all the details of upfront costs, not just rates, as well as requirements. Some of this depends on how much you want for how long. If a long time, you might want to do a fixed rate mortgage. (Lines of credit/equity loans are always variable, I think?)

Home equity line of credit is just that, a line of credit. Its like a credit card, with a much larger limit. The payments are usually calculated like a credit card too and higher than that of a Home equity loan, which is a regular amoritized loan.

It depends on what you are getting the loan for. If you are using the money to improve the home, then it might be a good idea to get, or if you are switching higher interest debt for lower interest.

I don't recommend getting a home equity loan to buy a car, or pay off student loan debt, etc.

I work in the lending industry and have for over 15 years.

In the end, debt free is better for you, unless you have a real need for the funds.