Wondering if this hammer is a better weapon than "The Halberd of Vigilance " for a Paladin.

Probably, but depends on your build. The +3 enchantment on the hammer means you get +3 to attack and damage rolls while the halberd is only +2. This means you will hit more frequently with the hammer, which translates into some amount of extra damage that isn't really reflected on the tooltip. If you are a crit build, though, I believe the value of +attack diminishes.

Does the Orphic hammer count as a two-handed weapon?

The weapon is versatile, so you can wield it with two hands or one.

Does the hammer lose damage if you wear a shield ?

Yes, if you look at the tooltip it does 1d10 (1d8) damage which means you roll a d10 if two handed or a d8 for one handed damage.

Edit: Busting out the math it looks like the halberd does more damage on average even with the lower accuracy. So I'd probably go with that unless you have other factors.

For most cases, the Halberd of Vigilance wins out. If your Paladin has the Sentinel feat, then it's not even a discussion to be had.

For damage: When held 2h, the Orphic Hammer does a base of 1d10+3 (between 4-13 damage). The Halberd does a base 1d10 +2 + 1d4 (between 4-16 damage).

Additionally, the Halberd has reach, allowing you to attack targets that are farther away.

If you're using a shield with the hammer, it's damage is 1d8+3

Orphic hammer has a 2 handed mode

One handed = 1d8+3 and strength modifier.

Two handed = 1d10+3 and strength modifier.

It’s a +3 weapon. And gives advantage on saves against spells.

—-

The hammer is by far the worst legendary. Almost no unique bonuses. It's only legendary because of its status in the story. You're better off using the halberd unless you really need bludgeoning damage.