There's a lot of other changes that each type gets to the numbers as well.Shell capacity Normal > Long > Wide.
Since normal has the most, doing an attack combo that leads to the big "unload every shell" slam is ideal. Long Shells do the most damage when you charge them up, Wide do the most damage just using a shell attack quickly and without charging. So whichever type you use denotes which gunlance play style you should follow.
Normal also gets a damage bonus to full-burst, in addition to being better because of more shells, and Wide gets damage bonuses for Wyvern's Fire and Wyrmstake. Also, each type gets different damage off of Wyrmstake Blast even when they use the same shell attacks, but I don't remember the numbers