When buying a drone I have 2 options to consider: brushed and brushless motors. Are they much different from each other? Does one have advantages over the other?
They are very different.
Brushed motors are good for toy grade drones for a couple of reasons: they are cheaper and don’t require ESCs, which would add extra cost and complexity.
However, in almost every way brushless motors are better: they produce much more power, are more efficient, produce more torque and, my favourite part, they don’t have physical brushes and so, unlike cheaper brushes motors which are only designed to run for a number of hours, brushless motors can take a lot of abuse and can last for years. Additionally, they are very water-resistant.
There are downsides: to a brushless motor - they require ESCs and, due to the torque, can do more damage in a crash.
For info on how each works, see my answer here: https://drones.stackexchange.com/a/87/50
At first brushed are fine because they are cheap and easy to replace. The more you read about specs and tuning you will take interest in brushless. For example betaflight now has rpm filtering which allows the gyro to reduce interference based on the rpm of the motors. So above tinywhoops and toys you are going to be seeing brushless.