So as not to cover other ground done by the other questions I will just say this:
Being a mage is fairly difficult at the start.. Its doable and I have stuck with it with characters, but your mage skills seem to go up so slowly. You really need to get around 40 destruction for the Impact perk before you will be able to feel in control of most combat situations instead of reactive to them. For comparison, a 2h power swing can stagger a good amount of time right from level 1.
Mages at later levels however are very powerful.. Not much more than any other type of play style (I have to admit that I applaud the ability to play this game in any style and never really feel put out by its limitations), but they definitely have a fun set of possibilities with their spells to make the game more interesting/amusing.
To touch on the note that you are seeing as well between 1h and 2h weapons vs destruction magic.. Please keep in mind that a Daedric weapon is equal to Master level spells.. Comparing it to Flames is a waste of time (get an iron dagger and compare it to flames :)). My character right now has fire/ice/lightning in her left hand and a nice daedric blade in her right (was ebony until last night :D). My sword is much more powerful than most of my spells (though I just got up to Adept level spells being half price so I am only just starting to fling fireballs at this point). This does not make my magic useless, as I can fling fireballs at things in the background, or right in my face, at the same time as I am slashing them down to finish off whatever health I may have... might also help my gear gives me +80% 1h damage while it can only reduce the costs of my spells, not make them more damaging.