When you re-finance with cash out to you, then your loan becomes what is called "cash-out" and some peculiar rules apply to it. Whenever you re-finance a cash-out, it stays a cash-out type of loan. This means that only certain lenders will be able to handle the transaction. So, once you do it, you'll be stuck with it for a long while. If you need more cash later, it's back to a lender who can do cash-outs to get it done. The transaction fees can mount up seriously. Just ask your lender about it before you decide on this.
HELOCs, on the other hand, have the advantage that you can pay them off, pay them down and make another withdrawal, withdraw a little and then some more later, and so on. That's a distinct advantage of lines of credit. However, a drawback is that the interest rate on the HELOC may vary. Maybe you get a great rate today and a year from now it's 9.9%. Still, you'll be happier with the limitations on HELOCs than on a credit card. Some HELOC even have a provision to convert them from variable to fixed rate. You can split the HELOC into more than one line and have a variable and a fixed, and so on. Also, the fees are extremely low.