Over the years, I've used chainsaws that run on gas, electric and battery. It's impossible to declare one "best" type, because such a choice really depends on one's circumstances.
The aspiring Paul Bunyans out there will almost assuredly want to go with a gas-powered type. With gas you have supreme power, and it's power you'll be craving if your intent is to go waltzing out into the woods to fell behemoths. You're tough stuff, so you don't mind if your machine is heavy, noisy and dirty (those considerations are for sissies).
Corded electric types have their place, but that place is most decidedly not any situation where mobility is paramount. Besides the inconvenience of dragging a cord around, imagine suffering a momentary lapse of control and slicing through the cord! No, corded models are for stationary cutting, as when you have a pile of branches stacked up next to a sawhorse that you need to cut down to size.
And what about battery-powered chainsaws, you ask? Well, I'm glad you're curious, because that's what my review of the Oregon PowerNow chainsaw is about. To whet your appetite, let me remark here that with battery-run units, you get the best of both worlds (gas and electric) to some degree. They start up like a charm (as with electric), but there's no cord to worry about (as with gas-powered chainsaws).