Tying shoelaces is a real challenge for bionic hands because it requires significant dexterity. For a hand to truly play its part in this task, it should have good hand speed and the ability to switch grips with ease.
The Michelangelo is widely considered the Cadillac of bionic hands and is likely the most expensive. It fairs a little better than the i-Limb but not enough to celebrate. For more information, see our Ottobock Michelangelo.
The Taska Hand is a fairly recent entry into the bionic hand market. At almost half the price, it fairs no worse at tying shoelaces than its priciest competitors. For more information, see Taska Hand.
All it all, it looks as if bionic hands still have a ways to go before they can tie shoelaces with the same dexterity as natural hands.
For a comprehensive description of all current upper-limb technologies, devices, and research, see our complete guide.