Anivia vs Orianna mid

It depends on the player. Both have rather high difficulty levels, with Anivia's being maxed out at 100. A decent Orianna will beat a decent Anivia, but a great Orianna will lose to a great Anivia.

Orianna has a vaccum, slow/speed up, and a shield that are all relatively straightforward in their use. Not to mention the actual orb itself as a ward and weapon.

Meanwhile Anivia has a skillshot Q that moves slowly, but can hit twice and slow/stun in an AoE upon detonation. However the slow projectile speed makes it tricky to land this attack consistently. She also has a wall for her W which scales in size with spell level and can be extremely tricky to place correctly, but can be used to secure a kill as well as escape. Anivia's E is what really sets her apart from Orianna though. Her E does double damage to an enemy recently hit by her Q or R, leading to some great combos if you can aim correctly with Q. Her R is a snowstorm AoE that deals damage per second and slows both movement and attack speed inside of it. It can be hard to use well because of how easy it is to just walk out of it, but you can use your Q and E to set up a sweet combo move if you're quick and once again have good aim with Q.

Tl;dr: An Anivia who can use her Q correctly consistently and land her E in time will beat all but the best Oriannas. And if that Anivia can use walls too, then Orianna has no hope. But Anivia is hard to use, so that's the drawback.

Also in teamfights an Anivia Q and R with Liandry's will wreck tanks and ADC's alike if they don't hightail it outta there quick.

Probably Orianna. She only needs to R -> W with her ball on a tank and you've won the teamfight. Anivia has to do much more just to matter.

Orianna is a stronger lane bully. Anivia is a stronger teamfighter. Relatively speaking.