256GB is high capacity (to me at least) I'd prefer a high capacity SSD speed USB drive over an external hard drive as it is easier to carry around, faster and less susceptible to damages from falling and general wear and tear
Keep in mind that SSD's are generally faster than USB's and the bottlenecks that will be in place such as the speed of the drive you're copying to or from and the interface you are doing it over (USB 2.0, USB 3.0, Thunderbolt, etc.).
