The straight answer is to do with the names given to the holes in Swiss Cheese, let’s deal with that first.

(…but there are SO MANY potential answers to the above question if taken as a joke, we’ve gotta come back to that, right?)

First: The Straight Answer:

The GOOD holes in Swiss Cheese are known as EYES. Potatoes have eyes.  (So do dinosaurs.)
I know you can cut a potato up into sections and plant each one with its own eye separately: they’ll each produce a new plant.
I don’t think cheese does this (I haven’t seen it happen to dinosaurs either).

The BAD holes in Cheese are known as “BLOWING” and are caused when the cheese develops gas, the kind that causes the cheese to explode right out of its side.
Catastrophically.
Not many potatoes do this, so the two reasons a Cheese might be like a Potato don’t really stand at all.
(SOMETHING happened to the dinosaurs, but It wasn’t their eyes and probably wasn’t indigestion.)

Tell you what, I need to stop now.

Post your punchlines in the comments below!

“When is a Cheese like a potato?”