For heroics, the bosses are the equivalent of level 82.
For raids, the bosses are the equivalent of level 83.

In PvP, you basically need 4% hit (more if they have talents to reduce your hit).
In PvE, its somewhere around 80 or 90 hit rating for Shammies or Druids to cap for heroics.
In PvE raids, you want 17% hit (for casters) and 8.5% hit for melee to cap.

1 hit, 1 crit, 1 haste, 1 penetration rating all cost the same amount of itemization points.
However a lower number for hit then the others gets you a 1% gain.
For this reason, until you're hit capped for your content, hit is the highest dps gains.
Once you're capped, hit doesn't do anything at all.

In general PvP gear has massive crit, resilience and stamina on it.
While these are useful stats, you could lose the resilience and a lot of the stamina and gain other stats for a PvE boost.
The honor bought PvP gear (Hateful) is equivalent to iLV 200 I believe.
That's the same as heroics or Naxx 10.
Deadly is 213, which is Naxx 25, or close to Ulduar 10.
Furious is the same iLV as Ulduar 25.
If you're already in full Furious or equivalent, you won't find PvE type upgrades until Ulduar 25 basically.

ToC Heroic, ToC 10/25 and Ulduar 25 will be better PvE type gear (at least in some slots) then what you have.

There will be the odd piece you can pick up, which will increase your PvE dps, despite being lower iLV.
But for the most part, what you have even if itemized wrong, is overall better then heroics/conquest items.

Concentrate on hit items, until you reach the hit cap.
Mana per 5 and raw spell power are upgrades for PvE.
A few trinkets which increase spell power on a crit or such, or the melee equivalent will be ups too.