Its traditional knowledge that equity financing is better for volatile business. The reason behind it that equity is permanent in comparison to debt which needs to be return after a fixed period. Thus even if situations are bad u dont have to return money in case of equity but have to so in case of debt. But the Debt financing is cheaper and thus help in reducing some extent of volatility and reduce risk
Suppose that you have the opportunity to finance a very very long term project with a perpetuity. I mean a bond on which you pay only a coupon but that will never be reimbursed... What difference with equity if the coupon rate is equal to the dividend rate and if no one intends to get his/her money back !!!