How can I defeat a Minecraft zombie that picked up my weapon and armor?

Place a boat in its path as it chases you, and get it to enter the boat - caught like that it's unable to chase you. At this point you could try slashing it with anything, but that will lead to considerable wear of the good equipment. Using a piston to push a block into its head instead, will quickly suffocate the zombie and finish it off.

An alternative is to box it in, in a small area, with blocks, then access from above and bury it in sand or gravel (dropping it by placing it against the ceiling above the zombie's head). Make sure not to allow it to climb up - place two sand blocks in quick succession, not to create staircase out of the box.

You can trap the zombie, and then use a falling anvil to inflict quite a bit of damage. You can then finish it off with something that has sharpness or flame, or even a decent bow. You can then repair the armor. Once you have it trapped, it's just a question of how to finish it off.

If you have cheats, just use /kill @e[type=Zombie]. That is the quickest way to do this.