Okay, I'll disagree! We've dined in the dining room several times and will do the Chef's Table for the fifth time in a few days. We much prefer the Chef's Table. Why?
Well, I wouldn't consider it a "ton of food", but we do like to try a variety of foods. With the Chef's Table, you get to try a little bit of almost everything on the menu that evening -- including a bit of caviar, etc. That makes it particularly fun for us.
We like the interaction with the chefs. They are without fail extremely skilled and delightful. We especially enjoy Aimee who has hosted our dinner several times.
Although I enjoy cooking immensely, I don't find being in the kitchen to be particularly enlightening. Needless to say, the chefs are very busy and doing their work, so I've never felt comfortable asking for a tour of the kitchen, a look at the ranges, etc. I'm sure they'd be willing, I just haven't wanted to be that much of a bother.
If you want a romantic dinner, I'd go for the dining room. It is quiet, luxurious, romantic and a harpist plays. The Chef's Table is not romantic in our opinion.
Nonetheless, given a choice between the dining room and the Chef's Table, we would take the Chef's Table every time. We do the wine pairings, DH and I get something different for each course, so we end up tasting lots of foods and lots of wines. For us, rather than cacophanous, it's the ultimate tasting/pairing meal. But the focus is on the food and wine, not the romance.
Hope this is helpful.