Well I'm a corsair and I know I have little standing amongst the Corsair Council of Elders but while I see the percieved need for this chart (a nod at Tenacity for taking the time), I feel from a personal perspective only, that I don't believe the Corsairs should use any Order tech except the Osiris which is really, as much Corsair as Order.
I do see however the Order getting access to our tech.
Why?
Well, on paper, the Order are much smaller than the Corsairs. They are a small secret highly advanced military outfit. Their tech is cutting edge (here read SNAC, armour and nomad weapons).
They fight 'the enemy without', the Nomads. The Nomads who just happen to be in Omicron Minor, Delta, Kappa, Omega 94 and Omicron Gamma. The Corsair home system. The Order are the only faction with the RP to 'Take it to 'em'.
Their enemies are the Liberty lawfuls, bounty hunters and Nomads. Infact, our hit list is very similar and their proximity is close to ours in Minor.
Corsairs on the other hand have some pretty fine and dandy weapons of their own and have little use of the Orders equipment, on top of which, the huge fleets the corsairs have couldn't really rely on those kinds of numbers of equipment coming through.
With regard to ships, I'd say no to each others ships unless a ship line was missing a class (and I don't consider the Carrier class to be an actual class). The Decurion for example is an ideal light fighter and, if the Order don't have one, they should use ours.
The only exception to this is the Osiris and I don't see that as ever changing.
Anything else should be special request. Full stop.
One other point I would make regarding the Corsair tech in the hands of the Order.
If at any point, some odd alliance got set up with an enemy of the Corsairs like GMG or Blood Dragons for example, all of that would stop and any existing weaponry would be lost to a lack of maintenance/spares etc.
Please note that it's just MY opinion voiced here and not that of any faction I fight alongside.