Like Eric, I would go with durations, the more recent spelll taking precedence while it lasts.
For real spell vs spell contests, that's another problem: At its core, the problem is simple: While Ars has Finesse as a measure of a spelll's Precision, it lacks any real mesure of a spell's strength(1).
So, lacking that, I would take a stance similar to Calllen's: consider the base effect (say, CrIg for +10 damage vs PeIg for +5 damage, CrIg wins out), or, if this isn't clear, the highest base would win. If there's a tie, I would probably go with the Penetration total, although I don't like it.
(1) Yes, My Ars Magica 6 would have 2 parameters for each spell: How much raw power it requires, and how complex it is to cast. In 5th, those 2 are subsumed in a spell's level
To the extent to which a spell is unopposed by the other, it takes effect. For example, if one spell turns the target into a hot stone, and the other into a blue piece of wood, the target becomes hot and blue - whether it becomes a hot blue stone, or a hot blue piece of wood.
To the extent the two spells are directly opposed, then if one spell produces an "objectively" stronger effect (say, The Unseen Porter is objectively stronger than The Unseen Arm), then the stronger effect wins. In this sense, outside circumstances can add strength to one of the two effects: e.g. you need much less force to keep a character on the ground than to lift him up into the air.
Otherwise (e.g. two spells trying to change the colour or the shape of a target) the effect with the highest Penetration wins. In case of a match, it comes to a coin flip, or it's a back and forth, depending on what makes for a better scene.
In some cases, Finesse can be used to appropriately "tweak" the result even by the weaker party - slightly altering the course of an arrow, or making sure that a single detail of a complex, contested illusion ends up in a certain way.
While some adjudication is often necessary, we've never found it really hard to come to a decision following the guidelines above.
there's also this bit I just saw in HoH: S p 98, Enchantment of the Pedestrian Pigeon says " A spell to read the thoughts of the target does not reveal the protected information unless its Penetration exceeds the spell’s level."
