Pearl Weapons vs Destroyer Weapons

As you noted, currently weapon stats (weapon damage, weapon stats, sigils) do not apply when using a weapon kit. Each weapon kit has its own weapon damage (scaled according to level).

However, ArenaNet has stated they are working on making sigils and weapon stats work with weapon kits.

I unfortunately don't have any specifics on the timing of specific abilities (such as the Bow's condition removal or each weapon's attack speed), but here's what I can tell you:

• Hammer of Wisdom auto-attacks, knocking back opponents on every third swing. Its active skill can be triggered to perform an on-demand knockdown.
• Sword of Justice auto-attacks, and can be activated to perform an AoE attack.
• Bow of Truth will automatically cure conditions on some sort of regular interval, and can be activated to create an AoE healing rain centered around the bow.
• Shield of the Avenger periodically creates a Shield of Absorption (with the same effects as the Guardian skill of the same name) centered around its location. In this video (@8:30), it appears that the first bubble is cast approximately five seconds after the shield is summoned, but that may have changed since that video was made. You can activate the shield to make it fly out (towards your current target?) and inflict Weakness on nearby enemies.
• All spirit weapons cannot be targeted or damaged by enemies.
• Activating any spirit weapon's "active ability" will destroy that weapon.
• All spirit weapons will despawn after a certain amount of time even if you don't use its active ability.
• You can have up to three spirit weapons active at a single time.