They are both equally bad. You are financing a risky (subject to gains and losses) investment with a risk-free (the loss in this case is constant) loan.
Is the 2nd method less risky given that the property is fully paid up?
No - even with a home equity loan you still pledge the house as collateral, so if you default on the loan the bank can foreclose on the home. You might not even be able to get a line of credit that large - the bank may prefer a traditional mortgage.
Mortgage interest is usually quite low and should not be too difficult to beat.
On average, yes. The problem is you're worried about "too much cash being locked up in the property" but not worried about cash being tied up in investments. Yes stocks and other investments are much more liquid, but suppose your investments drop 10% in a year (which is not unheard of). Now your total loss is 10% plus the paymenmts you have to withdraw to pay your mortgage.
Leverage (which is essentially what you're working with - borrowing money to multiply the amount invested) multiplies returns but it also multiplies losses. If you have a few bad years, you can end up losing your investment and your house if you can't make the mortgage payments.
A safer plan would be top pay off your house with cash and put whatever monthly payment you would have made on the loan into investments, preferably tax-advantaged investments like retirement accounts. You don't have to worry about making a fixed monthly mortgage payment, you build up your investment portfolio over time, and you have cash flow to get you through emergencies.