I'd agree in general, comparing fast food or quick serve style burgers, I prefer the smash style - if it's going to be thinner and well done, might as well have that nice crispy edge. But I love a fat, juicy rare burger if the meat is high quality - having a char-grilled exterior but a nice, red interior on a nice, fat inch-thick patty would be my favorite type of burger. Honestly though, it's easier to get that type at home by buying my own meat blends and cooking it on my grill.
The Geyser Point burger is in that good-meat, thick patty category, while the stack burger is in that thin, crispy style. Both delicious, in their own ways.