Why do we slice some meats thinly and not others?
Some meats are sliced thinly to break up the muscle fibers that run through it.  A properly sliced flank steak is tender, while unsliced or improperly sliced it's tough and chewy.  

Not all cuts of meat require the slicing, however.  If it doesn't have long, strong muscles, it may be fine without.   And this is a function of cooking.... tougher working muscles can. E slow cooked until it falls apart on its own, such as for pulled pork. 

Most cuts of meat from larger mammals may be sliced thickly or thinly, but the decisions soon often comes down to tradition more than anything else.  There may be national or regional dishes that prepare a specific cut of meat in a specific way.  Not only in how it's cut, but how it's prepared and possibly how it's presented and accompanying dishes.

When it comes to sandwiches, I'm of the opinion that shaved meat is always superior to sliced (except possibly when we're dealing with some that weren't a whole muscle to start... meatloaf, liverwurst, etc.... although salami, bologna, formed ham and many others are still better shaved). But I agree with Cindy that thick slices are often better when served on a plate.  (and more convenient to turn the leftovers into a casserole)