They are both effective at keeping your teeth sparkling if used correctly. They both have their own merits.
Mannual toothbrushes can make you feel you have more control, including the pressure it is on your teeth. This is helpful if you have sensitive teeth and gum, you may want to brush lighter over those areas. They are cheaper comparing to electric toothbrushs, making them easier to replace. They are also smaller in size, easier to pack when you are travelling.
Electric toothbrushes do lot of job for you with automatic rotation loosen your plaque. This is particularly useful for kids with poor dexterity such as kids, people with arthritis. The range of speeds can help you with your sensitivity. Some electric toothbrushes have warning light if you press too hard on your teeth. Electric toothbrushes seem more fun for kids who are reluctant to brush their teeth. Many electric toothbrushes have in-built timer to make sure you brush your teeth for at least two minutes and give guidance about where in your mouth you should be brushing.
For both types of toothbrushes, you should be replacing the heads every 3 months, or even more frequent if you are currently having ortho (braces) treatment. Your dentist will let you know if you have brushed adequately at your dental appointment and will tailor brushing techniques according to your needs.