OK, to be precise, the only common things between Gauntlet and CE are:
1-Both have top-down view
2-In both, you can direct the character in every 45 degrees.
Reason for 2 is simple, joysticks are made this way! This leaves us with the similarity in the perspective that means we can also relate every shoot'em up with space invaders and every console rpg with final fantasy 1.
You don't keep running into enemies in CE and expect to remain alive but in gauntlet, there's no official way to screw up your game. You can buy more energy with additional coins and the game doesn't imply how bad you're doing. Running into enemies is a part of the gameplay! Sure there are different characters to select but you also select from three characters in golden axe which is like.....UNREAL TOURNAMENT RIGHT!?!?!?!?!?!???!