Both Heroes’ have high tech high powered fortresses. A cool uniqueness is that they both live in their respective super hero strongholds. We've already declared the Batcave winner of this category, however it's to cool to not take a closer look!
Lego Robin said to Lego Batman, upon discovering the Bat Cave, “Wow Batman lives in Bruce Wayne’s basement?” The Lego Batman then replied “No Bruce Wayne lives in Batman’s Attic”.
Unlike his counterpart Bruce Wayne has really only shown us the Batcave! I'm sure he has a sky-rise luxury condo or two in Metropolis and Star City, but we don't get to visit that in the DC Universe.
What we do get is Wayne Manor and a ton of wicked awesome stuff in the Batcave! How about the T-Rex he keeps as a souvenir from an adventure on "Dinosaur Island" (Batman #35, 1946).

The Giant Penny you ask? Batman's encounter with a penny-obsessed villain named the Penny Plunderer (World's Finest Comics #30, 1947).

The Batcave is also loaded with tons of other "keepsakes" known as  "The Thousand and One Trophies of Batman!"
The Batcave has everything from all of the Bat Gadgets and Bat Modes of Transportation to a Super Duper Bat Computer! And of course Alfred is always around to serve his Master Wayne!


Tony actually lives in a home in Malibu where he kept some of his suits and tech. It got destroyed in Iron Man 3 when he gave up his home address to the Mandarin.

He also sometimes lays his head in a luxury high-rise apartment affixed to Stark Tower, which also got destroyed by the bad guys.
Then there is Avenger Tower, which is the Stark Tower renamed and remodeled after Loki and an alien army destroyed it in the battle in New York. Isn't that nice of Tony to let his fellow co-workers live with him!

I'm sure he and Pepper have some undisclosed, off the grid, remote, yet fully high tech'ed out mansions scattered across the world, where Tony can lay his head. We just don't know about those!

Then there is the Avenger Complex, where Vision walks through walls, Scarlett Witch does weird stuff, Captain America trains his ass off and the all the earth grounded avengers live like one happy family.

It's obvious that Tony gets around, and looks like he's had a lot of live-in headquarters as well!