Mentally, you may have a tougher time dealing with the monotony of the treadmill. (Here are some tricks for beating boredom on the treadmill.) Some runners think it's easier to distract themselves when running outside.
Of course, there are some benefits of treadmill running. Treadmills are a much better option than outdoor running when the conditions (bad weather, darkness) are dangerous. Many treadmills are padded, making them a good option if you're overweight or are injury-prone (especially with knee issues) and want to decrease the impact.
The bottom line: If you're training for a specific outdoor race, try to train outside as much as possible to get prepared for race conditions. If you're doing a lot of treadmill running, you can better simulate outdoor running by setting your treadmill at 1% incline.