I have a P8Z77-V Pro board, very much like yours. There are both Intel USB 2.0 and USB 3.0 connectors, and of course depending on your case you may or may not have USB 3.0 via the case front connectors. For sure, you have them available via the motherboard on the rear. And you also have the Asmedia USB 3.0 connectors on the rear.
So for sure, at the very least you need to use a USB 3.0 connector if you want to potentially obtain USB 3.0 transfer speeds. You're not going to get them using a USB 2.0 connector.
Second, external drives which claim to be USB 3.0 are actually SATA drives in an enclosure that provides a SATA->to->USB 3.0 interface. And depending on the external drive you've purchased, this may be a SATA-II or SATA-III drive. And of course every hard drive model varies in access speed specs as well as cache... some have as little as 8MB cache and some have as much as 64MB cache, and some drives are 5400 or 5900 or 7200 RPM (or even variable speed, in "green" drives). The fact that they have been placed into an enclosure facilitating a USB 3.0 interface doesn't change the capabilities of the drive for arm access motion speed as well as data transfer rate.
If you use a program such as
HD Tune (free or Pro) you will see the actual internal hard drive details (i.e. manufacturer and model) that's inside your external USB enclosure. If you then do a search on that drive id you'll see whether it's a really cheap or slow (or green) drive, which immediately is going to limit its performance even when using USB 3.0 connectors.
Just for example... I have two
Verbatim Store 'n' Save 2TB external USB 3.0 drives on my PC. Actually I've installed probably 10 of these drives (as backup drives on other machines for friends and family) over the past few years. Now even though these all purport to be from Verbatim, in fact every single external drive I've purchased has included a DIFFERENT brand/model of SATA drive inside it, starting with Samsung SATA-II drives, moving on to Seagate SATA-III drives, and most recently using Toshiba SATA-III drives.
Anyway, these two particular Verbatim drives are both Seagate inside... although two different drive models. Both drives are connected to the rear Intel USB 3.0 connectors on my P8Z77-V Pro board. And as you can see from the following screenshots from HD Tune (which show the particular Seagate drive model for each), they both perform differently.
In contrast, another Verbatim drive (this time with a Toshiba drive inside) in use by my Lenovo W530 laptop via its Intel USB 3.0 connector performs differently again.
Bottom line: all external USB 3.0 drives are NOT the same. But at least using an objective performance measuring tool like HD Tune can easily demonstrate what you should expect... in best case.
Note that in the real world, actual performance is a function of the type of data and record/block sizes. Doing a "backup" (say using Macrium Reflect taking a "system image") will produce superb performance, as might copying a very large multimedia audio/video file which individually might be hundreds or thousands of MB's in size. But copying hundreds or thousands of very much smaller files is not going to see the same performance.