Arcane and Frost both have points for, and against, them.
I will give you my perspective on which one is the better spec.
Arcane Arcane is the best spec for leveling if you will be doing a lot of single pulls.
The spec is very mana friendly, and is highly viable as soon as level 15 when you can max out Arcane Stability.
Arcane Stability simply allows you to cast your Arcane Missiles spell without being interrupted or having the cast knocked back, so you are guaranteed to shoot off 5 sets of missiles if your target lives long enough to survive.
Many Arcane specs will go into Fire early on for Pyroblast to give them a hard hitting spell.
This also serves the benefit of giving the build a little more survivability later on when you get the talent Presence of Mind (PoM), which makes your next spell an instant cast.
You can activate PoM and cast an instant cast Pyroblast to dish out quite a bit of instant damage to a target if things get rough.
This spec will lead with a Frostbolt (or Pyroblast if you spec into Fire), and then follow with another frostbolt or fireball.
From there you have some options depending on your target.
I liked to Frost Nova my target, jump backwards, and start casting Arcane Missiles until the target is dead.
If the target is about dead you can simply start casting Arcane Missiles after the second nuke.
As long as you attack one mob at a time, your mana should last at least a few fights.
Frost Frost spec is all about AoE grinding.
No doubt anyone who has leveled a character in WoW has come across a mage AoE leveling at some point or another.
It is an amazing sight to see, but also frustrating knowing that you will need to probably find another area to grind.
This spec will play a lot like a fire spec early on, except you will use frostbolt to keep the distance between you and your target.
It gains a lot of survivability later on to help you stay alive.
Best of all, the juicy AoE talents are kept in this tree.
Single target killing is slow as this spec, much like a fire spec is.
The real strength of a Frost build is in its AoE grinding ability.
A combination of talents like Improved Blizzard and Permafrost keep your targets slowed combined with Frost Nova if your victims get too close.
If you can AoE grind well, frost is the faster spec.
The downside is that you really need to look into bringing a priest with you to level for the shield and heals to keep things up.
Deaths while leveling will greatly slow your experience per hour rate, and must be avoided at all costs.
Avoiding death while AoE grinding is a delicate dance that not everyone can master (I will admit that I did not), so keep that in your mind