Both have pros and cons. If you’re on a budget, belt and pulleys is the best, it's also easy to repair/replace.
Source: internet, that link in particular
How does it work ?
An electric hub motor is quite simple: it's a wheel with a motor inside, with 3 wires coming out of it.
Unlike the usual electric motor where the stator (the "fixed" part of the motor) is the outer shell and the rotor (the "moving" part of the motor) the inner part of the motor, a hub motor works the other way around. The inner part is fixed to the truck of the board, and the outer shell is rotating around it. It's covered with a polyurethane coat that's used as a "tire".
Pros and Cons
- clean look
- less noise (the motor is inside the wheel and there are less moving parts)
- clearance (just the wheels and trucks, no extra parts around)
- no belt wear/break (of course, there’s no belt…)
- pushing the board is possible (maybe not true with all hub motors though; manually pushing with motors connected can damage the Vesc)
- easier to setup/assemble
- less parts required
- often dual-drive by default (2 motors per axle)
- good quality required, price++ (a cheap hub motor would likely break/fail easily)
- wheel and motor is one block
- gear ratio of 1:1
- motors can overheat more easily due to be enclosed in the wheel (which can make them fail)
- people recommend a 2 hub-motors drivetrain (to avoid overheating)
- The wheel material sometimes doesn’t stick well to the motor frame itself
- Requires specific trucks
How does it work ?
As the name says it all: it's a multiple parts system.
There are 2 pulleys: 1 that's fixed to the motor shaft and 1 that's fixed to the wheel. As you would have guessed, the belt transfers the rotation from one to the other.
The motor needs to be attached to the truck in order to move with it (when you turn, your truck stays flat on the ground but your board moves, so you can't attach the motor to the board itself). Due to the belt, the motor shaft and its pulley needs to be and stay exactly in front of the wheel pulley, and the two pulleys need to be parallel to each other. Using a belt doesn't allow for any movement to happen between the two pulleys (well, it does, but just a little).
If one pulley turns, the belt will transmit to the other to transfer energy. That work from the motor to the wheel, but also from the wheel to the motor for regenerative breaking.
Boards using this system can be single drive or dual drive (or even quad drive). On a single drive, it's better to have a big motor (63mm) to be sure to have enough torque. On a dual drive or more, 55mm motors are fine.
Pros and Cons
- cheap parts are not always a bad choice (you can buy cheap mount, belt and pulleys with a good motor and be all good)
- can replace each individual part
- adjustable gear ratio (use pulleys with different number of teeths)
- more torque (thanks to the gear ratio)
- takes 2 min to remove the belt and have a standard sk8
- single motor drivetrain is ok
- evolvability (each part can be changed for a better one later on; you can even go for a single motor at first and add another motor later)
- better efficiency (link)
- choose your own wheels
- more parts (more work to mount and more prone to something breaking)
- more maintenance
- belt will wear out
- pulleys can wear out (not if good quality though)
- requires some space around the truck and wheel
- requires good ground clearance
- not all trucks work with all mounts (you have to find a good fit)
- not all wheels work for that setup