Cons:
1) Speed to USB flash drive is slower than HDD
2) Your USB flash drive will wear out sooner

Explanation of #2:
Good flash media usually can only be written (erased, written is the procedure) to about a million times before degrading and wearing out. With all of the reading/writing to it, it will eventually wear out, and much sooner than it otherwise would have. http://www.fact-index.com/f/fl/flash_memory.html

Pros:
1) You can take your history anywhere