The only two abilities Morgana cares about (for her basic combo) are her Dark Binding (Q) and Tromented Soil (W). Her Q is 300 + 90% AP, her W's minimum total damage is 400 + 110% AP and is mostly considered as a waveclear tool or additional damage ability, if you hit someone with Q. Her ult is pretty scary, being able to deliver 600 + 140% AP damage for both the cast and second damage but that requires proper setup.
Her Black Shield, although not important in her damage dealing capabilities, is 350 + 70% AP. Her AP scaling is pretty high and her base damage is pretty high as well. But that's the thing.
She isn't really reliable as a mid lane mage. Her kit works but it's pretty basic. A lot of champions can just stay out of her range and not get blown up or they are mobile enough that they don't have to worry about her Q. Someone like Zed and Talon can circumvent her E completely.
Her support role is mediocre because of her utility and high base damage but getting off her ult is reliant on Zhonya's rush. And even getting off her Q doesn't mean the enemy will surely die. Since Zyra, Lulu and Karma dominate bot lane currently, Morgana is even less effective against them (Q blocking/evading, E easily penetrated if not leveled).
I main Morgana so this is purely from my standpoint.
Even if i know she's a decent mid laner, i don't generally take her there because there are simply better choices than her. If you look at her History on her lolwiki page, she did get some adjustments to her damage and mana costs (some minor stat adjustments as well) but that was purely because that particular time was when Morgana switched from being a mid laner to a support. Her last nerf was two years ago and it was a pretty minor one to Torrmented Soil. She hasn't been nerfed much in general.
Her old self VS her current self aren't that far apart in terms of damage.
Her kit is just old, strong in the right places but in most situations, "unusable".
That's pretty much it.