It's funny that White House in Atlantic City's sandwich construction came up. My friends and I have discussed this specific topic before at length.
I can name 20 different sandwich shops in NJ that use top quality meats, cheeses, veggies, etc. What WH does that shoots it up to the top 5 is the immaculate bread choice (strong enough to handle a beast of a sandwich) and the S-curve flip that they do with the meat to tuck it back into the sandwich.
There is a place in downtown NY next to where I work (Pane Peppe) that could be one of the greats. They have an excellent selection of breads, fantastic combos of meats, cheeses and toppings preselected on a huge menu (if your imagination sucks). They even have superb toppers like really, really tasty olive oil, real pesto or an amazing hot pepper spread. This place is legit. It's not cheap, but this is Manhattan where I've paid $8 for a Pabst Blue Ribbon in can at a bar. The only problem is the sandwich construction. There are maybe three guys out of a dozen in the store that can put a decent pile of bread and meat together and I mean they are just ok. You get the wrong guy there and you are going to be back at your desk, unrolling a soggy mess that is more like an italian Cobb salad with a giant roll for a crouton.
White House guys have always brought their A game when I'm there. I always think to myself, "there is no way this sandwich stays together while I eat it." And time and time again, they get it in there.
By the way, some ridiculous shops that deserve to be mentioned here:
Hoagie Haven (Princeton, NJ) - any place with a line out the door past midnight on any given night of the week speaks for itself - the bread alone is ~ 1,000 calories
Koch's (West Philadelphia, PA) - the line is crazy long and the guys aren't exactly working fast, but stand around for more than 5 minutes and meats and cheeses get passed around to try
Kelly's (Revere, MA) - my mom, a native to Boston, still swears by them - apparently, they're open on Christmas and there will be a line