I feel it is a mistake to pay "cash", or in this case use the equity in your own home to buy property, unless of course you simply have more money than you know what to do with.
By using leverage you significantly increase your cash on cash return. It will leave you the assets to qualify for future loans or additional cashflowing properties, etc.
The advantage to paying cash is that you don't have a mortgage, you can afford to carry a vacant property, etc.
In this scenario because you are not actually using cash you have in the bank collecting .000001% interest, you might compare what your actual payment will be on the HELOC vs a purchase loan.
It can be very challenging to get a cash out refinance after purchasing a property, some lenders can require 6-12 months seasoning to get your cash back out.
Just as an example, I took a call from a gentlemen today who purchased a home cash rehabbed with cash and was going to refinance. He lost his job and his life savings is tied up in a little property that rents for $875 a month that he cant get refinanced.
Just my 2 pennies. Good Luck!