Who's that handsome devil? BoredomIsFun's Storm Spirit guide!

Leveling remnant only increases the manacost and damage, while overload will give roughly the same amount of damage for no increase in manacost.
Ulti in (hit once), pull (hit once), remnant (hit once) (At this point 3 overloads, which means 45 damage extra per level compared to 40 damage extra per level with remnant.) From then on, every time you ulti, you can hit once too, notice how overload will eventually give more damage, while remnant is unreliable when you don't have the pull. At least that is how i figured it out. -Eyey

You have to be standing almost on top of your enemy to hit them with Remnant, it scales very poorly (140 damage at level 1 and only 260 damage at level 4, compare with most max-first nukes which are around 75 damage at level 1 and 300 damage at level 4), and it costs more mana with each level. As eyey mentioned, you will be hitting your opponent with 3+ Overloads when you combo them, making it scale better than Remnant. Also, while laning, you will rarely hit your opponent with Remnant unless they are melee. Remnant can be used to last hit creeps while Overload makes your harassment more powerful. -otaia