Mine wins yours, because of...

[deerhooves]

I don't know it will be fine, but anyway I'm going to try.
Rule is simple: XXX wins YYY, because of ZZZ.

Example)
Start with Dictionary
↓
Law book wins dictionary, because it's more thicker.
↓
Zippo wins law book, because it burns.
↓
Lantern wins zippo, because it's brighter.
↓
Curtain wins lantern, bcause it can cover light of lantern.
↓
...

And I'm going to add one more rule, don't be offensive. don't be annoying. Have fun.

I'm going to start with the Key.

 

[Minus]

Door wins key because it is heavier.

 

[Rosebolt]

Police wins Door because reasons.

 

[PenDragon]

Mob wins Police cause of treason.

 

[Mouse]

Mob wins cos of Teflon Don

 

[deerhooves]

Herd of cats wins mob, because it's more cute. :3

 

[Minus]

Rain wins cats because it scatters them.

 

[Mouse]

Cats win rain by sheltering beneath an old lady's skirt.