Assassin is actually easier to play than a mage. You will never get hit because your goal is to one-shot your enemies.
But assassins have a harder time against dragons.
I'm actually surprised you think that mages are powerful. When the game was just released, everyone was complaining that Destruction was weak. Has it been buffed?
90% of the destruction complaints are more acturatly worded as " I want spellmaking back". or those who feel that because some people abuse three different skills to create an adventurer's kit of godslaying +5 that they should be able to do the same exact thing relying on nothing but destruction itself. Wich ofcourse they could IF they had spellmaking. Thread after thread goes round and round on the subject. My mage is lvl 55, and i preffer destruction spells with her backed with some stealth and alchemy. I've died more often playing a two-handed meat tank or an assassin then I ever have with her. Most things get blasted to ash or run away screaming and on fire before they get close enough to hit. And if they DO get close, well thats what Fus Ro Dah is for lol.
-edit- if you're looking for raw damage, invest in lightning and take the disintegration perk. once that's taken lightning spells auto-kill enemies with 20% or less health. Even Sparks or Lightning Cloak will turn a wounded dragon to ash.
As for your assassin, unless you invest a lot of time and perks on archery or one handed the main challenge will be remaining undetected. You'll be able to one-shot most things from the shadows but crumble in a straight up fight. it's a fun way to play.