Because I was so confused when I found out it could learn both and I don't want to have both when I have other moves I want to teach it.
Neither. You need to teach it Sludge Bomb.
Sludge Bomb is STAB and has a chance to poison which is very helpful sometimes when you want to sap health from a foe.
Go with this set from Smogon:
Weezing @ Black Sludge
EV's: 252 HP 252 DEF. 4 SPA.
Shadow Ball, I find the SDef drop helps when taking down Pokemon.
I suggest you have this as your set:
Weezing @ Black Sludge (Leftovers works)
Evs: 252 Hp / 252 Special Defense / 4 Defense
~ Shadow Ball/Sludge Bomb
~ Clear Smog
~ Pain Split
I prefer sludge bomb over shadow ball but you want that anyways so
I would use dark pulse because of the chance of flinching, and to cover the psychic type weakness.