PIE does not affect the duration or the amount of DMG. The damage tics are based on the mobs HP and takes a percentage of it's max HP to calculate the damage. There is a cap to how much damage each DoT spell can inflict as well. So, while you're fighting a NM, the DoT spell is usually strong per tic when applied, but the spell is not going to stick as long as it would on a normal field mob because it's completed it's capped dmg amount so quickly. Still... even so, the damage done with these DoTs is a pretty healthy chunk of inflicted damage.

This is what makes DoT spells for THM incredibly deadly, overpowered, and one of the big reasons THM are such great soloers offensively. You can get by with just allocating 80PIE and use m.acc rings on top of an Ornate Scepter to save most of your points for capping VIT and having enough MND for a viable amount of MP. The modifiers through stat allocation are pretty marginal past a certain point anyway and you start to get diminishing results whether it be a melee or a mage anyway. This is why you mostly see VIT and MND builds with little focus on the att, acc, m.acc, m.att stat modifiers.

Long story short, atm stacking magical acc is superior to stacking PIE through gear. Let's not forget though that all of this will inevitably change in the future when they simplify stat modifiers and nerf DoTs. There is no question that it will be in effect very soon. Soon being when Japan gets back on their feet.