Keep in mind there's three speeds at play here;
USB 3.0 - 5Gbps
USB 3.1 Gen. 1 - 5Gbps (Essentially, USB 3.0 with a Type C connector)
USB 3.1 Gen. 2 - 10Gbps
Because of USB's overhead, it never approaches the theoretical max in a real world scenario. Back in the day, for example, 400Mbps FireWire 400 drives were MUCH faster than 480Mbps USB 2.0 drives.
For a single, standard hard drive, USB 3.0. For multiple hard drives in a striped configuration (such as RAID 0), then USB 3.1 Gen. 2 is a great option.
For around $150 you can get a two bay, USB 3.1 gen 2 drive, and then you can drop in a pair of standard hard drives in RAID 0, and get lots of storage at near SSD speeds for a fraction of the price. Note that this configuration would be for a 'working drive' configuration, and all data should be backed up continually. If one drive fails in a RAID0 configuration, then you lose ALL of the data from both drives.
With USB 3.1 gen 2, the only need to jump to Thunderbolt is really for multiple SSD's.
Also worth asking what it is you want to do. If you're just moving small files, occasionally; or using it as a backup/Time Capsule drive, then USB 3.0 is plenty sufficient.