A corded electric lawnmower seems like a great idea until the first time you get the cord wrapped around a tree. A cordless mower is one way to avoid such a predicament, but cordless mowers have plenty of their own drawbacks. The right electric mower for you and your lawn, either corded or cordless, depends on the compromises you're willing to make.
The most obvious advantage of a cordless mower over a corded model, presumably the reason that cordless mowers were invented in the first place, is the convenience of not having to drag a cord around the lawn behind you. With a corded mower, you always have to be within reach of an electrical outlet, and the range of your mower is limited by the length of your cord. The cord can be a nuisance, too, as it gets tangled around trees and other obstacles. A cordless mower isn't subject to any of these problems.
An advantage of dragging a corded mower's cord around is that it means you're always connected to a supply of power -- a corded mower never runs out of electricity as long as it's plugged in. A cordless mower will only keep operating as long as its battery charge holds out, which is usually somewhere between 30 and 90 minutes. That's long enough to mow a small- or medium-sized lawn, but if your battery gives out before you're done, you'll have to wait for a recharge before you can finish the job.
Corded electric mowers are typically lightweight compared to gas-powered mowers, so they're easy to push around the lawn. Cordless mowers have to bring aboard the extra weight of a battery, and batteries are heavy. Cordless mowers can weigh as much as 30 pounds more than a comparable corded mower.
Electric mowers in general are less powerful than the heftiest gas-powered mowers, and tall or wet grass can be a challenge for any electric mower. A cordless mower in particular may struggle to get through a heavy job, and as the heavy grass makes the mower work harder, the battery's charge will run out sooner.
The inclusion of a battery doesn't just add weight to a cordless mower. It also adds cost, and you'll pay a substantial premium for the convenience of losing the cord. A cordless mower may cost more than twice as much as a similar corded model.