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Because of the fact that bonds must be repaid and have a maturity date, this reduces the cost of debt.
With equity capital (shares) investors are exposed to a greater risk because there is no collateral supporting the investment and shareholders are last to receive money in the case of liquidation. Because of these higher risks, the cost of equity is generally higher than the cost of debt.
The demand for equity capital compared to debt depends on the company who is issuing the equity and the debt.
Because the interest on the debt is a legal obligation, the debt holder has more certainty that they will be paid. There is no obligation to pay anything to shareholders so there is more risk for shareholders, which increase the cost of the equity.