re: Karthus Q v Cassiopeia Q
Karthus:
40/60/80/100/120 (+30% AP) doubled if it hits only one enemy
1 second cooldown
20/26/32/38/44 Mana
200u center-center radius*
Cassiopeia:
75 / 115 / 155 / 195 / 235 (+ 45% AP) to all enemies over 3 seconds
4 second cooldown
40/45/50/55/60 Mana
75u edge-edge radius*
So by the looks of this, we can get off AT LEAST TWO Karthus Qs for every Cassiopeia Q. For the sake of missing being a thing, let's say that Karthus gets 2 Qs for every 1 of Cassiopeia's. That sounds a EXTREMELY biased towards Cassiopeia to me, since the truly fair ratio would be 4:1.
Cassiopeia will deal 75-235 (+45% AP). Cassiopeia will spend 40-60 Mana.
Karthus will deal 80-240 (+60% AP). If Karthus only hits one enemy with a Q, that enemy is going to take an additional 40-120 (+30% AP) damage. If he hits only one enemy with both Qs, that enemy will take a total of 160-480 (+120% AP) damage. Karthus will spend 40-88 Mana.
I FIND THE TRUTH TO BE SELF-EVIDENT FROM THE ABOVE.
Namely, that Karthus' Q is far superior damage-wise to Cassiopeia's.
However, the other nuances; lest they be forgotten for they are indeed important:
Cassiopeia's Q is fire-and-forget. You press it once every 4 seconds. It also has a nice haste on it, which allows you to engage or disengage. It enables Twin Fang to be used rapidly.
Karthus' Q requires you to mash it, once every second. Karthus' Q grants vision. Karthus' Q has burst damage (good for last-hits). Karthus' Q has a bit more range and probably slightly larger damage radius in absolute terms.
* AAs and some abilities are measured edge-to-edge, meaning that you can hit a 6-stack Cho with them stupidly easily, but center-center abilities have the same hitbox no matter the size of the edge of the foe (so it is NOT much easier to hit 6-stack than 0-stack Cho, if at all).