So I've been to Jiko once and actually thought it was quite good. I thought it would be a good "date" restaurant too. In fact I might give it the best marks of anyplace I've been so far. California Grill is a little too "bustling" for the romantic tag in my opinion (although the view is great). Yachtsman and Narcoosee's are great food and nice but the atmosphere is a little...plain. I haven't been to Artist Point. I feel like I'm forgetting someplace?
Some of the Epcot restaurants are nice.
We really loved Jiko when we were there recently. It's definitely a good date restaurant. 
I think what makes it different from the other high-end places is that it's so dark inside at night. That really added to the cozy, romantic feeling. Now, I might have a completely different theory if I'd been there while there was still light streaming into the huge wall of windows... .
I think the same would be true of Artist Point.
One place I haven't been and would like to try is Victoria and Albert's. Though I imagine that that much attention paid to me by one waiter would make it less of a date and more of a "threesome" 
I agree, a lot of the Epcot restaurants can be nice.
My opinion may have been aided by Jiko not being particularly busy while we were there.
Dark and quiet is always nice, and sometimes very hard to find in WDW.
I'd also say that the ribs were pretty darn good and that aided things as well!
I loved Jiko, even though I didn't feel well when we went. The kitchen made me a special dish of their famous mac-n-cheese even though it had been taken off of the menu. I would love to give this restaurant another try when I'm feeling well.
How do others feel about the romantic potential of Jiko?
We've been there twice and I think it is a very romantic place to dine. Very nice atmosphere and decor.