Its possible the drive might be more responsive when connected directly through SATA, but USB 3.0 has enough bandwidth likely to last until the death of HDD as a viable technology in the consumer space.
Many USB 3 controllers have historically been a point of weakness, however they've improved (and Intel now has USB 3 support on their newer chipsets) and you seem to have a new system so that shouldn't be an issue. The other point of weakness is the enclosure itself, however even if its a slower device, its probably fast enough for HDD speeds and I doubt tearing it down and installing the HDD into your computer will make it "much faster"
basically it comes down to potential convenience of being able to move that much portable storage, vs. marginally improved safety
if it was me, if I'm just going to be using it as a backup I'd keep it external, but if I was going to use it as another hard drive then I'd install it