Like some others above have said, mages struggle in the beginning, but as they reach the higher levels they steadily get stronger and stronger, until they suddenly hit a point where they can endlessly chain powerful spells because the relative magicka cost is so low. That, and power-boosting perks for spells, particuarly the Illusion tree -- which eventually lets you turn practically any foe. My current pure mage is an Illusionist, Destruction using vamp who also has powerful Conjuration magic. There's almost nothing he can't achieve, but he still gets pummeled by certain enemies; Volkihar Master Vampires, for example.
He's one-shotting Spriggans, for crying out loud! xD
I agree with Alduran. I think my magicka regeneration is nearly 400% now (with the restoration perks) but I play a vampire so it's pretty useless during the day anyway.

I rarely use magicka potions anyhow since I play a sneaky style mage. Once I'm invisible my regeneration returns to its full power and recharges pretty quickly.
Also, Alduran, gorgeous deviantart! Mind if I watch?

I don't know what's up with my vamp, but his h/m/s regenerates even during the day, but half as slow as at night. o3o
It's gotten to the point, though, that he can pretty much stand up against whatever he needs to, day or night, and only around level 55!
And thank you; I don't mind at all! x3