Here are just a few differences:
Bitcoins are an electronic form of money. Dollars are a physical form of money made of linen.
Bitcoins are limited in quantity. The Federal Reserve can create as many dollars as they want.
You can create a backup of your access to bitcoins. You can't create a backup of your dollars.
You can secure your access to your bitcoins with a password and cryptography. You can't encrypt your dollars.
It is much easier to store a large amount of bitcoins. It can be difficult to securely store a large amount of dollars.
You can send bitcoins over the internet. It is difficult and/or expensive to send dollars over significant distances.
I'll go for Bitcoin =)