I enjoy assassin characters more, but find them to be 1) slower (sneaking vs. running); and 2) weaker. A battlemage can stand up better to mobs imo. If you're playing vanilla, mobs aren't as much of a problem, but battlemages will still be stronger.
The assassin char build I prefer:
Race: Dark Elf (or Wood Elf or Argonian or Khajit)
Birthsign: Thief (or Shadow or Steed)
Specialization: Stealth
Attributes: Ag/Spd (or Luck or End or Str -- can't go wrong really)
Major Skills:
Sneak
Marksman
Alchemy (only if playing modded -- in vanilla, it levels waaaaaaaaaaaaay too fast)
Illusion (for handling mobs)
Conjuration (for support and meatshield; also can summon bows, weapons, etc. for sneaky killing -- don't have to carry the murder weapon on you)
Alteration (or Security) (for dealing with pesky locks, aiding encumberance, and sneaking into places via water)
Mysticism (only if playing modded -- levels pretty fast otherwise) (for detecting your target)
Last skill can also be flexible -- good ones are light armor, athletics, acrobatics (probably good to have one of the speed skills, esp. if playing modded), restoration, blade
The Battlemage build I prefer:
Race: Breton
Birthsign: The Steed (otherwise, end up being too slow, esp if playing modded) (or The Mage or The Apprentice or The Warrior)
Specialization: Combat (or Magic)
Attributes: Str/End
Major Skills:
Blade (or Blunt) (for melee killing and conserving magicka)
Block (for defense)
Heavy (for defense, may be less of a priority in vanilla)
Conjuration (for support)
Destruction (for ranged killing and also touch melee support and enchanting)
Illusion (for mob management -- frenzy, calm, command, etc.)
Restoration (for healing and buffs)
I'm currently playing dead-is-dead with the latter Breton Battlemage build using FCOM (overhaul mod) and nGCD (levelling mod) and am at level 7 alive and well, feeling confident completing quests and dungeon diving. Got a little hairy when mobbed by about 8 goblin shamans at one time, but fortunately, despite some mass paralysis on me, they didn't mob-destruction-spell me and I managed to survive by the skin of my teeth. Otherwise, things have been ok.
The problem with stealth archers, as has already been alluded to, is that if you get noticed and mobbed, things can be dicy. You have to be ready to run if necessary, which is why I like The Steed for stealth characters. In fact, FCOM has given me a whole new appreciation for The Steed birthsign
Ideally, you want to avoid this via sneak/marksman/alchemy and conjuration/illusion, but, especially at low levels, you still have to be pretty careful imo.
I love both builds to pieces though, especially with nGCD (essential mod imo).
It's kinda nice if you want to do both good battlemage (FG, MG, KotN) and evil assassin (TG, DB) playthroughs, rather than having one do-it-all character.