From the perspective of a lvl 40 mage, 90(11) destruction, fire and electricity damage enhanced, my alteration being 79(11) and alchemy 77 (7), 1-hand and bow 44/48 (o each) and lastly conjuration at 51(0).
The bulk of my perks (as you can see) being in destruction, alteration and alchemy. I have a few also in sneak and a few other key skills as well.
I am defiantly a sneak mage. I will sometimes open combat with a few double damage shots with my glass bow of the blaze (37 burn), or a melee sneak attack, Mehrun's Dagger, the Lucky Dagger and Dawnbreaker all have their points for this.
I expect if I had perks in 1-handed or archery the single target damage would be higher. With a few more points into sneak I'll have the 15x damage with the Lucky Dagger, that should hurt most things, or at least get their attention.
I do not find myself hindered killing with just destruction. Yes sometimes I have to spam lightning bolt or firebolt, impact is nifty and I can do either of those all day without running out of mana. Starting with some heavy hitting spells like thunderbolt or incinerate speeds things up nicely.
Then there are the times I walk into a room full of druagr, spiders, or whatever else. Fireball, chain-lightning, or ice-storm (even without the damage boost) eats crowds nicely. I dont see weapon skills doing the same.
I dont feel weak even in comparison to my friend who is a total assassin , he sneak attacks most anything in one shot. I have far more versatility -- or so I believe.
When I do find a tough fight I take a pot of +80% destruction, +90% health/mana regin, and others as needed. I end up selling most of the potions I find as I both make better and never get around to using them. Most dungeons I dont use any pots at all, if things get bad I take the two above pots and get real mean.
Be nice if spells had as much range as bows though, even if it is just a few 'sniper' type spells.

