I'm about the enchant an ebony bow (epic) with frost damage and noticed the only change according to the soul gem used is a slight difference in the charge bar (and price), though the amount of damage - in this case 31 points - stays the same. I understand the charge bar indicates how much charge is left on a weapon, but what's the difference when enchanting according to the soul gem used?

The level of the attack enchantment is based on your characters Enchanting skill, the amount of charges available is based on the soul gem you use.
There should also be an option to adjust the level of the attack enchantment so you can get more uses out of the weapon between recharging it.

Thanks!