Probably tmi, but here goes ...
Superman is from Krypton. He has incredible Strength. He flies under his own power. In the first Christopher Reeve film, Superman forced the Earth backward on its axis in order to turn back time to save Lois Lane from choking to death in her car in the California desert during an earthquake (!) He also redirects two nuclear bombs launched into the San Andreas Fault by Lex Luthor, which caused the earthquake in the first place. Superman is pretty awesome, although I'm not certain he's the most intelligent guy in the room ... Still, I think he wins any "fight" with Batman.
Bruce Wayne/ Batman is definitely highly intelligent and comes up with the BEST cars, boats, planes, toys and gadgets. Bruce Wayne has incredible charisma, but isn't vain. He values integrity and honesty. Batman's strong, but not as strong as Superman. He's human. I've always loved the Bat Cave. I enjoy(ed?) Gotham, seeing Bruce Wayne as a teenager. Sean Pertwee (son of the third Dr Who, Jon Pertwee), was an amazing choice to play the youngish Alfred the Butler.
The idea that Dr Who (which one? David Tennant, hopefully), could swoop into any Batman/ Superman confrontation with the TARDIS and disappear into a black hole is terrific! The Doctor could have saved Lois Lane without turning back time - unless he wanted to. The good Doctor is a genius. Because his IQ is so high, the Doctor can be ditzy when it comes to common sense, so he has to have at least one Companion traveling with him at all times. Suspect Special Forces training - self-defense, spycraft and espionage - is a very good idea for any Companion who wants to survive the Doctor's encounters with various creepy entities - ha! My all-time favorite Dr Who episode is The Girl in the Fireplace. Tennant plays the Doctor. Blink is another terrific episode, again with Tennant. I also like the Tom Baker episode where the Doctor's Companion, Adric the exceptional mathematician, crashes into Earth in a spaceship, creating Iceland and killing the dinosaurs 65 million years ago.
My avatar is the Firebird, from the Russian ballet. I don't know if there's much difference between a Firebird and a Phoenix.