Onions is a top example for me.
It is one of those "accent foods" that is a staple to any good burger, hot dog, steak sandwich that I might eat. One would think that if you like an onion then you'll like it regardless of how it's cut. Yet, I find the onion to be a prime case of texture and even psychology making all the difference in how it is enjoyed.
Quite simply, I prefer diced onions on any burger or food item. I'm not a fan of the thick rings that are merely sliced in circular fashion. My guess is that this has something to do with the impression of surface area tasted on the onion. I find the tiny diced bits to "harmonize" better within the burger's overall ingredients and feel that diced onions don't over-saturate the mouth with onion flavor as much as the bigger ring slices. In other words, diced onions seem to spread out their flavoring better while also being less "intense" or strong in any given bite. Somehow, the same onion cut into rings can give a whole different/stronger taste to the same burger.
I also love finely diced onions on a hot dog (for instance) instead of the bigger sliced "chunks" or onion pieces that sometimes are cut for such foods. I also tend to like sauteed and caramelized onions and thus diced onions seem to suit such actions better (at least in the foods I enjoy most).
In summary, it can be fascinating how textures and shapes of certain foods can impact our impression of taste and overall enjoyment. The onion may be a prime example of this but it isn't the only one! Some other foods that I distinctly find "different" just because of their texture or use include:
Apples over Applesauce - I enjoy a fresh apple. I just don't like the mushy/sweetened texture of applesauce however. One actually tastes quite different than the other to me...
Hard Tacos (shells) over Soft - Another big one for me. I need the CRUNCH! There's also the element of the CORN taste in a hard shell mingling with the beef, cheese, etc. I don't get that preferred corn crunch with the soft, flour tortilla. To me that "corn crunch" is kind of what makes a taco a "taco" and so its never quite the same when the hard shell isn't there...
Tomato Sauce over Tomatoes - This is sort of the opposite situation of my apple over applesauce preference. In this case the "sauce" wins. I enjoy certain Italian foods and pizzas thus my idea of the tomatoe's zenith exists in sauce form. On the other hand, I rarely eat a real, fresh tomato. It just isn't the same tasty thing to me in its original form for some reason...
Hard Ice Cream over Soft (melted) - Another big texture/shape thing going on here. I prefer the very hard, parlor-style ice cream where the texture is near solid, gummy-like (in the positive sense), you can bite or lick it and the ice cream is firm and frigid. I'll eat a soft serve cone as well but its really a different thing to me. I miss the chewy hardness texture and find it to just be more like a tasty sugar cream soup rather than ICE CREAM. Both have their place but I'm definitely more in the hard/chewy camp.
Well, that's probably enough rambling and lists for now. Feel free to place your own "onion vote" or add to the above list

Jeff