I think I summed it up quite nicely above, if I do say so myself.
Anyway, it's for a desktop machine that I need the extra storage, I already got an external HDD for my laptop and it served well enough… until it dies. So, I'm not sure I want to make the same mistake twice.
Any words of experience from the venerable elders?
If you're looking for reliability, you're pretty much on the same track no matter which of the two options you choose. There's about the same chance that an external hard drive will suddenly die on you from some undetected condition as is there for an internal one, no guarantees. So:
If you're looking for just a small bit of extra space, go cheap with a small external.
If you're looking for a huge amount of space, go all-out and invest in a huge internal.