Hub-motor
Pros
- Cheap
- Reliable
- Low running costs
- Power doesn't depend on gears
- You can keep your gearing
Cons
- Weight towards the back is not so good for exceptionally steep hills, like you get for serious off-road stuff. It makes the bike wheelie.
- Power has a fixed range of speed, so you have to choose one that gives its power at your modal riding speed. Too slow, and it runs inefficiently; too fast, and the motor maxes out, so no power
- More thought, planning and adjustment to fit than a mid-drive
Crank-drive
pros
- Weight in the centre gives sharp handling for tight off-road stuff.
- Power depends on gearing, so you can get the power at any speed and climb exceptionally steep hills with the right gearing.
- Easy to fit.
Cons
- Faster wear and more chance of failures with the drive train. Any drive train issues will leave you stranded.
- You have to be in the right gear all the time, which makes riding more frantic and less relaxing.
- More expensive
- Higher running costs due to wear and other drive train issues.
- You normally have to change your front gearing - no triple chain rings
Some people will mention the difference in efficiencies. My tests show that that's false.
Some people will mention the extra difficulty in taking off a hub-motor wheel, but that isn't an issue. You fix punctures with the wheel on and if you fit a puncture resistant tyre, you'll probably never have to take the wheel off in the lifetime of the bike. Mine's been off once in 6 years, and even them, it didn't need it.
I always advise people to get a hub-motor for riding on the road and light trails, and a crank motor if you want to do serious off-road riding.