AD Cassiopeia has:
- No mana problems, when she runs out of mana she can still deal damage, but even that happens rarely in 3v3.
- Very high damage with Trinity Force
- The Phage passive and Noxious Blast grant her a lot of movement speed, kite potential
- High poke, high burst and damage over time in combination with an ultimate that can stun
- High auto attack range (550)
- Hybrid penetration works very well since she deals almost as much magic as physical damage overall. It makes her much more viable.
- A lot more damage in mid game

AP Cassiopeia has:
- More burst
- A little bit more range
- More late game damage
- Way easier to play since you only spam abilities
- Doesn't get focused as hard, people are really scared of AD Cassiopeia since the animations make her look like a monster.

This kind of build became more powerful with the Trinity Force changes. In combination with Trinity Force, Sorcerer's Shoes are the best choice, they give a huge damage bonus in early to mid game, people do that on Corki, Ezreal and Kog'Maw already, champions that deal a lot of magic damage while not needing the attack speed from Berserker's Greaves because of the Sheen proc.

I put a focus on the Trinity Force and Sorcerer's Shoes to make her a scary beast early-mid game. Basically you continue the build very similarly to Corki, going for increased Crit chance with Infinity Edge and building Last Whisper very early after that, you can go for LW before IE. The reason I go for Statikk Shiv is not only because of attack speed (which is ok but not neccessary, it gives crit chance most importantly and deals magic damage (!) with the passive that works with magic penetration which is included in this build. For the last item you may need a Blade of the Ruined King to deal more damage against health stackers, it's a core item against tanks, if you can't afford it early enough or if you need something defensive because you have no frontline in your team (which happens often in solo queue) go for either Randuin's Omen against AD teams or Spirit Visage / Banshee's Veil against magic damage teams, Banshee's also grants you cooldown reduction which is very useful. Against hybrid damage teams you can go for only health items like Frozen Mallet or Overlord's Bloodmail. Frozen Mallet gives you a nice kiting bonus while Overlord's Bloodmail is way cheaper and gives you health for kills. Moonflair Spellblade is pretty awesome on Cassio since you get damage, hybrid resistance and tenactiy while only costing 2300 gold.

I really like to go for hybrid penetration runes and hybrid penetration on the offense mastery tree. For masteries I also take points in crit masts because of the very high crit chance after Infinity edge. The defensive tree depends a lot on the matchup, you may change it.