External SSD drive vs Flash drive (USB 3.0)

20GB per machine * 50 machines = 1 terrabyte of space.

At the moment, these drives are pricey, if you can even find one. I'd settle for a smaller size SSD for your internal drive, and then look for a pair of e-SATA drives enclosures holding something like this:
http://www.newegg.com/Product/Product.aspx?Item=N82E16822148591&cm_re=momentus-xt-_-22-148-591-_-Product

While I assume you're referring to a solid state hard drive, I'll point out that most thumb drives use solid state technology as well. Performance is usually slower for thumbdrives as they use slower controllers, but you can find some that use the same SandForce controller used in most solid state hard drives.

The advantages of a real solid state hard drive over a non-SandForce thumbdrive would most likely be speed and price per GB.

Compared to a SandForce based thumb drive, the SSD would be bigger, heavier, and require an external enclosure or adapter.

I'd say if you're looking for speed and weight, go with a SandForce based thumbdrive, though you'll pay a premium for them.