Heh, some variant of "Shivering Touch" would probably come up in every one of those scenarios, since it's available by level 5 and instant kills dragons (especially with a lesser rod of maximize). Plus, Spectral Hand is a level 2 spell that ensures you don't have to get close to use it. I don't really want to get into every exact combination of class and scenario simply because it takes a long time, but suffice to say the usual problem of "if you think about the scenario, there's some spell that deals with that scenario" comes up.
Another question: I guess the tiers only compare the pure class abilities, not the class abilities combined with standard equipment (as per wbl). Am I correct?
To an extent, yes. It's only about classes. Sometimes a particular piece of gear works better for one class than another (for example, a Lesser Rod of Maximize is only useful to people who have a class that casts spells) and so that might be factored in a bit, but I wanted this to be a general case tool, so I didn't want to make any assumptions about what gear you might have. After all, some people play with magic marts around every corner, some play by RAW (where most marts don't necessarily have all you need and most gear is randomly dropped), and some play where getting the exact item you want when you need it is almost impossible. I wanted it to apply to everyone, so gear's not really factored in here one way or the other. Besides, if one party member has all the gear they want, the other probably does too, so it balances out. Remember, this is about how classes work together in a party... it's not about PvP arena battles where one tries to kill the other. The question is "in a given scenario, how useful is this class" not "who's better than who?" The point is that players have more fun when they all feel like they're working together, while they get frustrated if one person is the star and someone else just feels like a henchman.
As for Dread Necromancers... last time I played one from level 1 to level 12, while it was a solid contributer it was obviously not as strong as the Sorcerer (who was clearly leaving it in the dust by level 10) and yet was obviously a fine fit with the Beguiler and Swordsage who were in the party. While DNs have a solid list of spells, they rely on the DM giving them good monsters to reanimate... if that doesn't happen, there's not much you can do about it. Planar Binding doesn't come with the necessary control spells so all you get out of that at the mid levels is some drastically under CR'd skeletons and maybe some useful transport (skeletal Nightmares provide flying mounts). Getting a huge amount of skeletons isn't actually all that helpful... unless you get something really good to reanimate (like a 10 headed hydra or a really high HD giant) those guys basically become cannon fodder that gets in the way, and most of the really good zombies/skeletons are too big to fit in a lot of medium sized dungeons. Grabbing the right Advanced Learning spells can help (Animate Dread Warrior is AMAZING if the DM ever throws a decent humanoid at you, while Ghoul Glyph, Black Sand, and Shivering Touch are all solid), but in general DNs are one of those classes that boil down to "if the DM hits me with stuff I can use they're great, otherwise not so much."
And I have to wonder about the "but they could totally use feats to get Magic Circle and Dimensional Anchor on their spell list!" Well, yes, but should I rank a Warmage at T2 because he can do the same thing and get Planar Binding too? What about Monks? They can cross class UMD and get wands and scrolls of Planar Binding, Magic Circle, and so on as well! Where does this end? The simple answer is to look back at the original post and note that I said "equivalent optimization." If we're comparing Dread Necromancers with the necessary two Arcane Disciples to get the spells to Planar Bind Efrettis and such, then we should be comparing them to a Sorcerer who uses Mage of the Arcane Order to get more spells on his list (that's about equivalent) and can do the exact thing... plus cast the rest of the Wizard list. The DN is still behind, and noticeably so. Whatever you do with optimization for one, do it for the rest too before comparing.
Meanwhile, the Favored Soul can have whatever the strongest Cleric spells allowed in your game are. That's absolutely amazing. The Favored Soul is much like the Sorcerer... it only looks underpowered if you're used to playing with the T1 version (Cleric or Wizard, respectively). Judged on their own merits, they're amazing.
And note that I don't assume all Factotums have FoI. It's common as heck, but the more I've played that class, the more I've realized you really don't need that feat.
JaronK