Shulk can see and alter the future, Terra can't. Shulk would definitely win.

Also, Terra has to wait for her turn, Shulk attacks whenever he wants!

Shulk is heavily dependent on his teammates, though. He needs someone to draw aggro so he can stab the blind spots of opponents. On his own, he gets into trouble. He also loses a ton of his power fighting living organisms as opposed to machines.

Shulk also has to wait for his turn.  He attacks automatically within certain intervals of speed and has to wait a cool down time in order in order to be able to react again.

Shulk can attack at the exact same time as a badguy, If an enemy is even a split second faster than Terra, she stands and waits for the enemy to complete his attack. Shulk's cool down time only applies to his special abilities.

Terra can equip two relics at once so there so there are multiple possibilities of what she can do.  Economizer reduces MP cost to one for every spell.  Gembox allows to cast a spell twice.  Genji glove allows to equip two weapons.  Offering allows four attacks from a single weapon, if combined with genji glove then eight attacks. 

Terra can equip the paladin shield and absorb every elemental spell.  She also learns merton(meltdown) at a high level without the need of an esper damages all opponents and is fire based.  Merton can't be reflected so one of the possible relics to equip would be the reflect ring which would allow her to regain full health and damage opponents each turn while gaining full health at the same time. 

This isn't her skills

Turn her into an imp with all imp equipment, including the shield so no genji glove she can't use magic but will have receive one damage from all physical attacks, have high magic defense, so equip her with offering and reflect ring.  Four attacks, magic reflects off her.  If she can't use magic and she's by herself what does it matter if  auto reflect is on? 

Economizer and Gembox allow her to cast two spells each turn for 1mp each.  The spell quick lets her go three turns in a row.  On the third turn, you can cast quick again and it'll work again, allowing for possible an infinite amount of turns in a  row.  Ultima/quick, ultima/ultima, ultima/ultima, repeat at ultima/quick.  Or economizer and offering so 1mp and four attacks.  Quick, merton if HP not full, attack x 4 with the atma weapon for 9999 damage each hit, repeat at quick.

Morph doubles her stats but it doesn't last forever. 

Terra can also cast invisible which works 100% and spells like break, doom, etc are guaranteed to work.  Works on bosses as well.  If the enemy is immune to the spell, invisible/x-zone will still work.

His premonitions would make all of this pretty much obsolete. All he has to do is evade until he can attack, then Terra stops dead in her tracks. Plus during fights she doesn't move or evade very well. This wouldn't be a marathon of baraged attacks, it would be a sprint of quick percise attacks and evasion. Terra is very emotionally unstable, and not very quick witted. Shulk would see her weakness instantly and it'd be over before it began.

Who then? I need a JRPG character.

From what I played, it was heavily dependant on me, not my teammates (the AI for your teammates isn't that good).

Bolded: Only applies to the unlocked Monado (the one unable to attack the Face mechon). Monado II on Prison Island and Monado III (Shulk's Monado) have equal power among all things. This is why Shulk os able to defeat the organic God Zanza.

For more info, I copied the info of the Monodo II:
The Monado II is a weapon in Xenoblade Chronicles. It is obtained on Prison Island just before the fight with Metal Face. Zanza breaks the shackles that made the Monado unable to cut sentient Bionis life. In fact, the Monado, after the upgrade into the Monado II, becomes a two-cut weapon. It also allows the Monado's skills to be upgraded to level 10. With Monado II, Shulk can also attack any Face Mechon and being of Bionis without rebound as they are piloted by Homs.

His most powerful attack still is more effective against machines. It's not bad against living targets, but it's definitely not in the Omnislash/Aether/V-create tier. On any other main character in an RPG, it would be his or her best damage dealing move before learning the ultimate move.

Show an example of this. The end boss was not a machine, he wouldn't take a weapon that is better effective against machines into battle. The Mechons had a Monado as well, was that better against machines? The only one that was more effective against machines was Monado I. Also, there are only desperation attacks in FFVI (if I'm not mistaken) which rarely hit the enemy. It would never hit Shulk.

In XBC gameplay, your teammates are heavily dependent on you because like you said, the AI isn't all that. But that's not a Shulk thing, that's a gameplay thing. Anyone will tell you that if you're going to have Shulk (and especially Melia) in your party, you'll want to control them because Shulk is all about setting up his teammates for topple-lock and protecting them through visions and spike removal, two things the AI is horrible about. He will struggle to be the primary damage dealer in most combinations, and if he happens to be main muscle and drawing tons of aggro, then you're doing it wrong. He's not built to take or deliver consistent damage: he delivers it in spurts by stabbing the enemie's sides and back by keeping low aggro, and buffing/empowering his teammates in the meantime.

This has more to do with your strategy in the game. The gems, equipment, armor, and link abilities (which effects are still given even if teammates are not in battle) would be more than enough with the Monoado's leveled up skills to hold his own in battle.

Therefore, he makes a pretty poor fighter one-on-one, which is not good for a death battle. I'm not discounting his ability to see danger ahead of time and alter the future, but there's a gameplay limit on how often he can spam that ability. And if he wants to do anything significant to actually alter the outcome of events, guess what? He has to use some of that talent gauge, which has to be so full in order for him to see visions and alter outcomes. So he's contantly trying to balance offense vs. survival.

With a proper loadout, it would not be hard at all for him to fight one on one.

I don't know he matches up against Terra Branford, because I've never played FFVI (one day, one day). All I can do is analyze Shulk.

They are both powerful, but Shulk is a fast, percise, tactical fighter who runs in to battle. Terra on the other hand is an emotional mess who typically flees from danger.

Invisible (which never misses because it is a positive status effect, but it can be cast on enemies) has the side effect of decreasing magic evasion to 0. So cast invisible, then doom (or cheat as much as you want with the gem box, economizer, quick and whatever spell you want). Game.

Terra dodges better than Shulk could ever dream. Due to a glitch mblock is used for physical and magical evade calculations, and she can max it with the right equipment. A character with max mblock dodges everything that can be avoided 100% of the time.

This is assuming Shulk is standing around while Terra is casting all this stuff. She wouldn't survive long enough to kill Shulk. But let's say he never even lands a hit, Terra's Magic and Physical attack power maxes out at 255.

(Not Terra, but stats maxed out at 255 in FFVI)

Shulk would never feel her attacks

It'd be like fighting a fly on the wall.