The two spells are similar in nature, they help protect you from damage taken from an energy type.
An arrow of acid springs from your hand and speeds to its target. You must succeed on a ranged touch attack to hit your target. The arrow deals 2d4 points of acid damage with no splash damage. For every three caster levels you possess, the acid, unless neutralized, lasts for another round (to a maximum of 6 additional rounds at 18th level), dealing another 2d4 points of damage in each round.
This abjuration grants a creature limited protection from damage of whichever one of five energy types you select: acid, cold, electricity, fire, or sonic. The subject gains resist energy 10 against the energy type chosen, meaning that each time the creature is subjected to such damage (whether from a natural or magical source), that damage is reduced by 10 points before being applied to the creature's hit points. The value of the energy resistance granted increases to 20 points at 7th level and to a maximum of 30 points at 11th level. The spell protects the recipient's equipment as well.
Protection from energy grants temporary immunity to the type of energy you specify when you cast it (acid, cold, electricity, fire, or sonic). When the spell absorbs 12 points per caster level of energy damage (to a maximum of 120 points at 10th level), it is discharged.
Since both spells would protect you from the energy damage of the acid arrow (assuming you cast the correct form), is the acid neutralized or does it still exist?