A company that is unwilling to give up control of the business is in need of additional capital. Would issuing additional stock or issuing bonds be better for the company?

Issuing bonds will be the better option for this company. Mainly because they do not like to give up the control of the company or to change its equity structure.

When the bonds are issued, the company gets the money from the investors and has to pay an agreed amount of interest periodically until maturity of the bond, where the company will have to pay the face value of the bonds.