My character is a level 17 nord that uses longswords. Which is a better enchantment for my weapon, damage health, or shock damage?

I would go with the "Damage Health" enchantment. While this can be resisted by only "Resist Magicka" items and spells, Shock also can be resisted with "Resist Shock". So a shock spell has a higher chance of a percentage of it being resisted.

This is my educated opinion, and could be incorrect. Just an FYI.

I know this will probably get some flack, but IMO the most powerful enchantment for any melee weapon is...

Soul trap 1 sec on strike
Drain Health 100 pts 1 sec on strike
Weakness to Magic 100 % 5 sec on strike

You will get 20 uses with it if you enchant using a grand soul gem, and take down most enemies in a few strikes.

About the same. While it is correct that there are a few more enemies that resist shock damage, it is a cheaper effect to enchant with. This means more charges on the your weapon or more damage for the same number of charges. Base cost of shock damage is 7.8; base cost of damage health is 12.0.

Honestly, either is a pretty good choice. If you're enchanting at the altar, consider adding a brief soul trap effect to help with recharging.

For some reason I'm getting the feeling that this is a choice between two sigil stones that ilovelamp has. If that's the case, I'd also consider which of the two had the more useful defensive spell, and take that into consideration when making the choice. There are two different Sigil Stones with shock damage, I believe; One of them has Shock Shield, and the other has Night Eye, as their alternate effects. Both of those are good. The Damage Health sigil only has Fortify Health as its alternative, and I question the value of that, unless you're playing a low-health character. So, if it's a case of sigil stones, I guess I'd vote for the Damage Health.

Having said that, I like the Shock Damage better between the two, if only because I like the appearance of the effect when it hits.

Ha! I bet your right, about the stones. Good thinking. Instead of giving an answer to the OP's question, I rattled off some nonsense about an enchantment list.

@ OP: Sorry about that. What ever the case may be, the shock is more fun. I don't think there's enough difference between them to make a choice other than preferred effect.

Absorb Health 15pts 1sec+Absorb Fatigue 20pts 1sec+Soul Trap 1sec.(Azura's Star)
I find this works great,especially since I use a Fine Steel Longsword,with it's rather low base damage these enchantments make it a good sword for higher levels.

One point about shock: many daedra are weak versus shock, so if you plan to face lots of daedra, that may be an additional incentive.

If you progress another 10 levels, you'll probably replace your weapon, anyway.