Windows will buffer the writing for as long as it can, so the first chunk will write faster than the rest. The display is showing the over-all average so it is initially high and slowly drops down towards the actual write speed of the flash drive which is presumably a little under 5.8MB/s.
Even though Windows default to not holding writes for USB drives like this in cache for long (written data is flushed to disk a small amount of time or immediately when the file is closed), it will still buffer writing a little while there is active writing still going on and also the copy operation may have its own buffer so it will keep reading as fast as it can until this is full, so the initial speed will look faster then the over-all speed. This is also why the copy progress display will sometimes sit at 100% for a second or two after a long write operation - as the copy operation closes the file the call to the "close" function blocks until the final few blocks of data have been written.
It is possible to tell the OS to perform completely unbuffered write operations, but very little code does this (Windows Explorer doesn't) as it stands in the way of a number of potential small optimisations (in the OS and the drive's controller) that can speed up write operations.
Yes, there will be a difference.
As far as I am aware the faster USB flash drives tend to be around 20MB/s write speed (but speed varies a lot depending on manufacturer and controller) while hard drives tend to pretty much saturate the USB port and transfer near the limit at around 40-50MB/s
Hard drives are much faster at bulk data transfers, while Flash devices tend to be much faster at finding small bits of data quickly.
EDIT
To answer your comment
You can get some portable 500GB drives that will work from USB bus power alone, they tend to be based on laptop hard drives and can be a bit slower than the full size hard drives, but generally they're fine. An example is this one.
A full format can take quite a while and it only takes longer the larger the drive is, with an approximate 500GB drive I would expect a full format to be of the order of 3 hours at USB speeds
(500*1024)Mbytes / 40MBytes/s = 12800 seconds
= 213 minutes
= 3.5 hours (approx)
It may end up being a bit faster (something like 2.5 hours) due to getting slightly better speeds (USB can theoretically get up to 60MB/sec, but there are protocol overheads and other devices that share that speed), manufacturer megabytes (as manufacturers do not measure a megabyte the same way everyone else does) and other factors. Heck, it may even take longer if it's a particularly slow drive or the USB bus is doing other things....
Generally though, USB drives come preformatted, have protection (S.M.A.R.T.) so that if they fail to write a sector they will remap the sector out of the usable portion of the drive, and a quick format will suffice 99% of the time.
Best Answer
A simple check on Wikipedia can help a lot:
So indeed reading from a flash memory will cause it to rewrite some blocks every now and then. Writing to a flash memory happens block wise, and every block can only be rewritten a certain amount of times (actual number differs). But considering that this number is quite high, the drive manages (wear leveling) the writes to be evenly spread across the drive, and only every 100th or so read uses a write, your drive will probably die of other reasons before. Or you will just dump it, because it has gotten too small.
So my recommendation would be: As long as the drive is fast enough, use it instead of the hard drive, unless you want the movie on the hdd anyway.