I thought a really long time about how and why to write this conclusion to this series, but in the end this is how I decided to go with it.
If we are judging Annie vs Soraka based solely on the support role, than Soraka is definitely the better support. These are a few of the definitions of support from the free online dictionary.
To bear the weight of, especially from below
to hold in position to keep from falling, sinking or slipping
To be capable of bearing; withstand
To provide for or maintain, by supplying with money or necessities
to act in a secondary or subordinate role to a leading performer.
Simply put, in all of these roles, Soraka does better. Notice how there is no mention of providing opportunities, or killing enemies. Killing enemies is not in the job description of a support. If the adc makes a mistake, she is able to keep him in lane by healing him. She gives the adc mana so that the adc is able to act in his role better. When Soraka and an ADC lane, the adc gets stronger with Soraka supporting him, whereas with Annie, the ADC and Annie become separate entities as the game draws on, becaming an ADC and a mage. In other words, the adc scales better with Soraka as a support.
The way that people think of bottom lane is fundamentally wrong right now. When you are playing Annie bot, you are not playing a support role, but rather one of a mage. The role of a mage is to provide balance to the damage output of the game by dishing out magic damage, and by playing bot instead of mid, you are trading gold potential in return for utility. Mages scale with levels and since you will mostly be fighting adc's bot lane, who scale with gold, you will have an advantage over them.
This is in no way advocating that support + adc lanes are better than adc + mage lanes, because the fact of the matter is, in some ways, mage + adc lanes are better than support + adc lanes, better burst for example. But in a way, this is like comparing apples and oranges. The flavor of the lane is different, and they can only be compared in certain aspects, because they are fundamentally different.
The distinction doesn't matter in most cases, except when you are playing against the opposite number.
The fact of the matter is, it's hard to say where the line between mage and support begins and ends for certain champions. In some ways they are the same. It is merely convention and tradition that seperates them. For example, Taric heals, buffs and debuffs, and peels with his stun, but also does a lot of damage with his ult, passive, and shatter. But everyone agrees he is support, because of convention, even though Taric top does very well. But you can't just draw a line in the sand and say “These champions are support and these are mages”, because you lose out on a lot of potential by doing so.
In the end, I think it's not a matter of which champion is better, but rather knowing everything your champion can do, and using your champion to their best potential.