Agree or disagree? Just from an amount of icons approach, not taking into account how they might manipulate the struggles (adding/deducting, changing which icon struggle get resolved, etc.).

Terror Struggle:

#1: Hastur. Yeah, big shocker. Actually, can he take the first two spots on his own?

#2: Shub-Niggurath

#3: Cthulhu

Combat Struggle:

#1: Agency.

#2: Yog-Sothoth. Odd pick? I was all ready to write Yog off, but after adding more APs to the mix and seeing all those C icons on the Gugs, Yog can pack a lot of them.

#3: Cthulhu

Arcane Struggle (this one I have most trouble ranking the factions):

#1: Hastur

#2: Yog-Sothoth

#3: Miskatonic? Cthulhu?

Hell, I'm not even sure if the first two are the "right" ones. Yog is supposed to be good at Arcane Struggle, but haven't seen him surge ahead of the pack really.

Investigation Struggle:

#1: Miskatonic. Like Hastur rules Terror, Miskatonic has Investigation Struggle by the balls.

#2: Syndicate

#3: Agency

From my limited experience, I'd say Miskatonic dominates the investigation struggle even more than Hastur dominates the Terror struggle. It's just a vague impression, but I'd say that Cthulhu and others have more insanity icons than Syndicate has investigation. Ideally, I suppose you'd also have to take into account the most useful strategies for each faction, and whether or not these are likely to focus on a given struggle.

Cthulhu is surprisingly low on terror, due to the deep ones having CCA, pushing the faction more towards combat and arcane.

Yog is rather combat heavy as well. Even before the LCG format it had theBloated Star Vampire bringing in 4 skill, 4 combat for 3. (and some awesome art!)

Syndicate is all about well-roundedness, allowing any icon to appear.

Yog is also surprisingly investigation-heavy, because some of the Elder Things. Shub can do this too - traditionally some Mi-Go carried investigation into Shub. For Cthulhu and Hastur it's a big no-no though.