Flash Drive or External HDD?

From a price perspective you can't beat an external drive. There are many manufacturers putting out pocket size drives as well. I've had luck with Western Digital and Seagate. Try to stay away from drives that use propriatory automatic back up software.

Look for a nice 500gb external drive on sale, and with the money saved pick up a 16gb flash drive for pure convenience.

Bare in mind that defragging / multiple writes will kill a flas drive a lot quicker than a 'normal' spinner...

Defragging flash drives is useless. If you're that worried about it, transfer the data off, format it and load everything back up.

Most of the time you lose the damn thing before the write cycles are used up.

From a brand quality perspective, definitely Western Digital for external HDD, good value for money and extremely reliable. (I've a My Book for around 3 years now, never any problems), you probably want to go with the My Passport model (for portability's sake) and to be honest I'd go with a bigger external HDD than a 32GB flash drive, I don't think you'd notice THAT much difference tbh.....

Flash drives are generally slow, particularly for writing large files. The WD here is a cheap bare bones Elements, size of a pack of cards.

Let me add, that the speed is determined by the actual connection. The flash drives are usually USB 2. This is a slow (or at least, nowadays slow) connection, although mjf's numbers look way slow to me, my SanDisk Cruzer something gives 20 MB/s on average, but that's besides the point. Internally, both the HDD in external drives and flash memory are way faster than USB 2, so that's your bottleneck.

Personally I use external HDD for backup and storage, and flash drives for smaller files, video (to play on Blu-Ray player) and so on. I use external HDD with eSATA connection, that's way faster than USB 2. In fact, I can't understand why most external drives sold on the market are USB 2 instead of eSATA. Now comes USB 3, it's faster than eSATA but not by much. In any case, the theoretical speeds of both eSATA and USB 3 can probably only be achieved on solid state drives, as usual HDDs are slower than that.

USB 2 speed limitations are a factor particularly for external HDDs. Most of them are actually sata drives inside the case. I think there is more going on with USB flash drives. My tentative conclusions are that the R/W storage devices in the USB flash drives are the main speed limiting factor. Also I notice that speed can vary for different flash drives.
Here is my result for SanDisk Cruzer 4GB. Somewhat faster than the Lexar but still not a substitute for the external HDD for general mass storage.