Two of Xenoblade Chronicle's big stars! Let's see how their stats and abilities hold up.
We're likely using Monado III Shulk, and Rex with Pneuma (that's his highest tier, and he's never alone).
Attack Potency: Shulk's at Universe Level+, but so is Rex.
Durability: Both are at Universe level+, so even.
Speed: Shulk is FTL+ (much faster than light), and Rex is likely FTL+.
Shulk's Monado gives him the ability to see into the future, allowing him to act to get a better outcome. He's also got Monado Arts, which include Shield (nullifies attacks), Speed (increased speed and reaction), Armour (reduces damage taken), Eater (removes enemy buffs and inflicts bleed), and Buster (a powerful slash that deals more damage to Mechon). He's also got a few other arts, but let's move on to Rex. Not listing all of them.
Rex also has foresight, but also the ability to lock a command, elemental attacks, and flight. However, he does have the weakness of if Pnuema dies, Rex will be physically damaged a lot, maybe even die.
So in conclusion... this is tough. But Shulk's got enough versatility to definitely go around Rex's command locking, and can reduce his damage taken. I'm not sure how strong Pnuema herself is, but Shulk can likely dispatch of her easier than Rex, if he can land a hit on her. Between Rex and Shulk, however, Shulk likely takes it. They both share numerous abilities, but the ones Shulk's Monado has definitely could be what gives him the win.
I'm voting Shulk wins.