Shake Shack burgers are just decent and overpriced for what they are, but the fries really set them apart. They're always perfectly crispy and well-seasoned/salted.
Five Guys, OTOH, are floppy/soggy and not always salty enough. Never understood the hype. I think people get all excited because of the quantity, but I'll take quality over quantity any day - especially when it's an empty calorie item.
The thing about salt, personal preferences vary. One can always add salt to taste, but you can't really take it off if you get too much (though I have tried). I like Five Guys because they are fresh cut, include the skins and they use fresh peanut oil which I prefer. I haven't tried Shake Shack so can't comment. I do agree that Five Guys can be floppy, perhaps could be a bit crisper but they are good as is. One thing I hate, those fries that have starch coating which is intended to keep the exterior crispy. WTF is that stuff anyway? Just another example of excessive processing that isn't making things better.
Bringing home Five Guys (or any fries, really), they of course cool off and lose some of the initial appeal. Put them on a cookie sheet and broil for a minute or whatever and they are rejuvenated.
Spelunkers has already been mentioned - they have excellent fries though much more modest quantity. They also have real milk shakes -so you can go burger, shake, fries and it's all going to be excellent. In Vienna, Plaka Grill kicks ass with their gyros and a single portion of fries is a large amount (good for 2) as well as has an interesting seasoning. They are thinner fries so they cool off fast on the ride home.