A USB3 port can supply up to 0.9 amps, more than USB2. But that still is not usually enough to power a larger HDD commonly used in desktop machines. Even to get that working, you would need to buy an enclosure or dock designed with a USB3 interface plus a USB3 hub that is powered by a power supply module that comes with the hub.
Now, USB3 is much faster than USB2 for data transfer with a computer IF the host computer also has a USB3 port. If the host has only USB2 (VERY common on older desktops and laptops), a USB3 enclosure for your 1TB HDD will work, but only at the slower USB2 speeds that you are used to.
I think your better choice would be a docking station (easy to change HDD units) or an enclosure (better protection for the HDD mounted inside) that can accept SATA units and has a USB3 data connection to the host computer, but ALSO comes with its own power supply so that any HDD installed can receive all the power it needs. That way any SATA HDD can work with that, plus you will get faster transfer rates IF the host computer you're working with happens to have a USB3 port. In fact, some docks or enclosures are able to accept either the desktop standard size 3½" form factor HDD or the smaller 2½" size common in laptops. Don't worry about SATA I, II or III (now called SATA 1.5, 3.0 and 6.0 Gb/s) specs. They are all backwards compatible, and there are NO standard mechanical hard drives (spinning platters and moving heads) that can even get up to the SATA 3.0 Gb/s data rate. Only the best SSD's can exceed that spec.
Example Docks:
http://www.newegg.com/Product/Product.aspx?Item=0VN-0003-000H5&cm_re=hard_drive_dock-_-0VN-0003-000H5-_-Product
Handles any SATA HDD, has USB3 and its own power brick; good user reviews
http://www.newegg.com/Product/Product.aspx?Item=N82E16817198056&cm_re=hard_drive_dock-_-17-198-056-_-Product
similar to above, but also can accept old IDE hard drives.
Sample Enclosure:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817198056&cm_re=hard_drive_dock-_-17-198-056-_-Product
Handles 3½" SATA drives but not 2½", has USB3, own power supply; good user reviews