I've aggregated some numbers for you guys and I can give some answers on when PvP gear can be used in lieu of full PvE gear.
Using a DPS marauder, I compiled the following builds PvE and PvP builds, using stock modifications and with a small emphasis on Strength and Power when given the option (e.g. in implants and relics):
Black Hole MK-1
Elite War Hero
(for fresh 50s with 99x Tionese Commendations and free MK-2 gear)
Alternatively, you can read the combined stats of all the builds through this spreadsheet
that I crudely made.
With the numbers side by side, we can make some reasonable hypotheses:
1. Full Recruit MK-2 players can complete most Tier 1 HM flashpoints and Tier 1 SM operations (as DPS).
The overall base damage between full Tionese and Full Recruit MK-2 are pretty close. The Tionese build will be slightly better because the relics are on-use, which will give short periods of additional DPS. A Tionese/Recruit hybrid will output considerably more damage than a person in full Tionese, but will still be slightly below a full Columi player.
2. Full War Hero players can complete all flashpoints and all Tier 1 operations on any difficulty, EC SM and TFB SM (as DPS).
War Hero players can actually out-DPS Rakata players. If the Rakata player used the on-proc relics whenever it was available, the DPS difference may not be that significant.
3. You should not bring War Hero gear to EC HM or TFB HM (as DPS).
While the evidence suggests that you should be able meet the DPS requirements for these operations, other factors such as your health will start to reduce your overall survivability in most boss fights, which typically require players to take damage no matter how good you are. The uselessness of expertise in PvE content are highlighted significantly in these modes and only gets worse as you progress through the operation.
4. PvP gear has no place in EC NiM.
Don't even try.
I have not compiled numbers for tanks and healers but the results should be roughly similar. I only did DPS because that is the majority of most players.
Remember, gear is not the end-all factor to determining a player's ability to complete PvE content. If three players in Tionese/Recruit gear can complete HM LI without using companions
, you have no excuse.