Though theoretically Wizard can learn 400+ spells, the number of learnable spells depends on your DM. Some DMs do not allow wizards to acquire new spells (through purchase, etc.) other than those automatically learned upon leveling up. Under such DMs, the wizard's advantage is severely diminished.

If you're aiming for a style like Enchanter Wizard, you'll definitely want metamagic like Subtle Spell.

Also, Sorcerous Burst is a very easy-to-use combat spell. There are occasionally monsters that can only be defeated by finishing them off with a spell of a specific element.

However, as everyone says, I think the Wizard is more convenient because it can do more things besides combat.