While the Battle Pike was almost objectively the coolest looking building (YOU HAVE TO WALK INTO THE MOUTH OF A GIANT FRICKIN' SNAKE! It felt like going on a demented Disneyland ride!), and I loved the exploration element of the Battle Pyramid, by far the one I used most was the Battle Factory.
For one, it meant I could hop into a heated battle at any time, no matter what the levels of my mains were. And secondly, I really liked the clever twist that you could switch out one Pokemon from each person you defeated, so you still got that sense of your party slowly evolving over time. It was a really well-designed formula.