Supposedly, mages are ideal for extended team fights, while assassins are ideal for eliminating single, vulnerable targets (mages and maksmen).
A mage is able do an assassin's job while an assassin can't do a mage's job.
Another problem for assassins is the fact that mobility means little in the current meta. Pings and vision easily spoil an assassin's roam, which also ruins the assassin's cs.
Assassins that go all or nothing (Talon) have high risks, while assassins that hit and run(Zed, Kha' Zix) are more safer and more forgiving.
Mobility is EXTREMELY important in the current meta. Ever notice why champions like Lee Sin, Yasuo, and Lucian are high priority picks in competitive play? Their mobility allows them to dodge cc and position around teamfights since the pace of the game has increased drastically since its release. This is why champs like Varus and Ashe have fallen completely out of play since they cannot postition around teamfight or kite bruisers and assassins. Lee Sin was super overpowerd when he first came out not only because his early game damage was absurd (since there were other champions that had tons of damage), but also because he was one of the most mobile champs at the time. Ever since he arrived, they've made a lot moe champions with gap closers like Zed, Riven, and even Kha'Zix that can jump around teamfights to increase their effectiveness.
Mages tend deal less damage overall, but do it to multiple targets and nearly constantly. A good example of this is Ziggs
, who's main damage tool is his Bouncing Bomb that packs a good punch with a short cooldown. He also has a giant mutha-fuckin Mega-Inferno Bomb to drop onto all his enemies. Usually mages cannot kill individual target's quickly without their ultimate. This is defnitely true on Ziggs, as well as Lux
and Annie
. This leads to the problem with mages as assassins being that since their job is to provide constant damage to multiple enemies, it is extremely wasteful to use their longer cooldowns, such as their big ultimates like Mega-Inferno Bomb, Final Spark, Summon Tibbers, and Pyroclasm, on single targets, since it is a huge part of their large AOE burst. Usually assassins either a) can perform a killing combo without their ultimate like Fizz
or Kha'Zix
or b) get their ultimate up very quickly (at least at stages of the game) like Akali
(fucking hate her stupid buillshit kit) and Kassadin
. Also, mages tend to be a lot more immobile than assassins, which as I said before is a huge part of the current meta; it makes it very easy for mages to get caught and killed and also prevents them from repositioning in teamfighs. Ex. It is very difficut for an Annie to perform her combo to the full potential since she lacks a gap closer and has to use Flash
to get into range, and whenever she is caught out of position she usually has to burn Flash to get reposition, a huge sacrifice. This is why Ahri
is beginning to pick up steam again, since she is very mobile with a lot of burst and a good cc ability.