As long as there is power at the work site, plugged-in power tools will always have power, giving you a full day's work. Cordless tools run on a battery pack. Batteries have a limited life before they need recharging.
Although it may not seem at first glance to be an issue, working all day with a heavy tool is tiring. Corded tools are lighter. The problem is the battery. Technology has not managed to produce a battery that lasts yet is still lightweight and small. Centered balance of cordless tools is not always easy to achieve because of the battery size, making it harder to work with all day long.
Corded power tools are designed to push the power out. An unlimited power supply allows the tool to complete heavy-duty jobs like drilling holes in concrete all day long. Cordless drills have power limits and are designed to conserve as much power as possible to last as long as possible between recharges. This reduces the cordless tools' effectiveness to light or medium jobs.
Corded tools are usually less expensive than cordless ones. Batteries for cordless tools die after a while and need to be replaced. These batteries can sometimes cost almost as much as a new cordless tool. Battery chargers also fail and need to be replaced. Another factor in cost is can you afford the down time on the job while waiting for the batteries to recharge. Over time a cordless tool can be expensive to own.
Last but not least is freedom of movement. Mobility is the deciding factor in many instances. With corded tools there is not always a plug handy, and extension cords are dangerous. Even worse, there may not even be power at the site. Cordless tools allow you the freedom of movement no matter where the job is without the worries of getting power for the job at hand. Many feel mobility outweighs the power of a corded tool.