You have a good guide here, but it does need to be finished up. Of course, I do recognize that it's still in progress (that's hard to miss, really) but I think that overall it's a good guide, with lots of potential. I must say, though, that I don't know that I agree with your "Pro" when you said she has the best Ult in the game. I'm sorry, but that's not true. I have played a fair amount of Cass, and when you compare her to Champs with "God ultimates" *stares at Darius* then it's simply not true. I know it's a small thing, but just something I thought I would point out.

nice guide

As to why I prefer Athenes Unholy Grail over an Early tear of the goddess to an archangel's staff, although Athene's got nerfed quite hard, it still gives more ability power and mana
regeneration over Archangel's staff. Yes, you can get Tear early and build it into archangels later, it will take quite a while to get full stacks of it to make it into Seraph's embrace. This is because there is a 3 second cooldown which means that your burst would only give you 5 mana(4 mana with tear) cause your burst is definitely less than 3 seconds unless you use your ultimate to try to go for the kill, which is 10 mana(8 mana with tear). As Cassiopeia, you shouldn't be spamming your Q to harass your opponent or it will cause you to unnecessarily push your lane, which leaves you vulnerable for jungler ganks. I like to find opportunities to do some burst to my opponent then have my mana regenerate for me. Archangel's staff gives you AP based on the amount of mana you have, but even if upgraded to seraph's embrace, if you swap it with athenes in my build, it gives you about 2150 mana, which is about 64.5 extra AP. It seems nice at first, but remember it takes a lot of times to stack up unless you spam spells every 3 seconds, which no one would probably do. I feel that it takes too long to upgrade it to Seraph's Embrace, which is a better item than Archangels only because of its shield. However, Athene's has 3 unique passives I like a lot. Firstly, it has 15% cooldown reduction, which allows Cass to spam her spells more. It restores 12% of your max mana for every kill or assist you get, so it means that even if you expended all your mana to get a kill or assist, you still have enough to get more kills or to escape with your miasma or your Petrifying Gaze if you need to. And its 3rd unique passive makes you get Veigar's passive for free. The fact that Athenes has better base stats than Archangels, has better unique passives than Archangels Staff and Archangels Staff takes a lot of time to build into a Seraph's embrace makes Athenes a more viable item. If you find opportunities to put down your burst and not try to spam your spells and push the lane unnecessarily then even without blue buff then you will not face mana problems. However, for lanes that you need to max your Q first like Fizz and Kassadin then if you cannot get blue buff Archangels Staff is definitely viable.

This is a pretty good guide, and i know it's still in progress, but i do have a question:
What do you think about an early Tear of the Godess which you then turn into an Archangel Staff? I think this is a really good item on Cassiopeia since she is very mana hungry, and because you can spam your Q to farm or harass, you will also charge that Archangel Staff really quickly, and that should solve her mana issues. (At least with me, it did).