Assassin help.

[Valyn]

Alright, so I'm trying to decide between these two builds for my new assassin I'm going to make.
Build 1: Main skills: Sneak, one handed, archery, light armor, and alchemy. Just your average Wood Elf archer/assassin.

Build 2: Main skills: sneak, one handed, illusion, light armor and alchemy. This one is a bit more complex. Usually start off with a frenzy spell, and wait 'till they kill each other, and then finish off the survivor. And when things get rough, cast a calm spell, and then sneak behind them and slit their throat. Or, just cast invisibility and kill them all.

Theres not much difference between these builds, except archery and illusion, but I want to know which one is more fun to play as. I haven't done any assassins, so I don't really know that much about them, so ANY feedback is welcome.

 

[Bumblebee Jones]

Whenever I'm an assassin I use an argonian

I choose the bow with a dagger on the side

dagger is incredibly efficient once you get the x15 dagger sneak attacks perk

 

[FruitsPonchiSamuraiG]

I did the first build on my first playthough and it was quite fun, dual-weilding the daggers once it got rough was the best...

Now I'm playing a character kinda like your 2nd build, but I'm going completely mage. So, I don't use one-handed. Conjuration comes in handy here.
Like you said, I start off with a Rage spell, let them kill each other BUT if there's anyone left I summon a Flame Atronach to do the job for me. If you go far enough with Illusion you can get a perk that silences every spell you cast so you can cast whatever you want from the shadows.
I hardly get my hands dirty, but if things get tougher than what I can handle, I always have a follower or two waiting for me somewhere.