They're all decently well balanced (around defeating bosses).
Learn their strengths and weaknesses and use whichever you prefer.

The following comparison is being made only for MAX level magic.
This is because I'm lazy.

It's also because all magic has pros and cons that are not damage related.
This is why I suggest that you learn more about them and use whatever you like.

These were my stats during testing (yes, I love glass cannons):

All tests were done on 1 (one) enemy, and without hitting weak spots (hitting those deals 50% more damage). They were done in Advanced mode, on NG+, on v1.0.5.

The results for regular shots:

The results for casting:
Note: the mana cost for casting magic is not the true cost. This is because your mana keeps regenerating during your cast. This means that the longer your cast, and the faster your mana regen, the cheaper they will appear to be.

Out of the regular shots:

• Fire slaps the hardest, but has to be used up close;
  
• Lightning is the best for mid and long range, but is really expensive;
  
• Ice goes pew pew really fast;
  
• Arcane is the magic you start with.

Casting deals more damage per mana (and is also my favourite way to kill bosses):

• Arcane has the best damage ratio, but you also have to shoot it 3 times, which is very slow. I don't know if it's possible to cast the others more than once (maybe if you level up Haste to MAX?), but if it is then they will all outperform Arcane;
  
• Ice's shards are divided amongst all chosen enemies, so it's not better at targeting many strong foes. However, it has very powerful passive buffs;
  
• Fire homes in on the chosen enemy and has very good tracking. Additionally, it sucks in nearby non-boss(?) enemies, but can also hurt you. Its passive buffs can turn our little witch into a melee maniac;
  
• Lightning has a large radius, but targets an area on the ground, which can sometimes result in skill issues. However it slows down time, so that can help;
  
• The big hit of both Fire and Lightning will usually stagger bosses. Arcane staggers too, but I'm not sure if it works on everyone.

On an unrelated note...
The casting chant changes depending on how much Haste you have.
Here's a person translating all versions to English.