For what it's worth I think a joint ownership would work more in favour of EXT than BRS.
I can't see easyJet transferring its operations from BRS to EXT because the latter's catchment area is so much smaller. I could see EXT receiving the odd easyJet flight from another base in the way that BOH is about to be serviced by a GVA-based a/c.
Where I think EXT might score is in what you suggest - long haul charters. If the same company owns both EXT and BRS why would they bother to waste too much time trying to fly out of Lulsgate when they had a more suitable runway just down the road?
On the other hand if someone else owns EXT the BRS management would fight tooth and nail to secure such flights over a rival airport even if it meant making offers to airlines/travel companies "too good to refuse."
I also think a joint owner would try to rationalise the use of the two airports and use them as complements, and that EXT in percentage terms, if not in actual ones, would get the best of the deal.
BRS is about to break the 5 million annual pax barrier and the management reckons it can handle up to 9 million with an extension of the current terminal and the provision of up to about 30 aircraft stands (it's got around 23 or so at present I believe).
EXT is approaching the 3/4 million barrier and could easily double this in the next 2-3 years, and who is to say what could be achieved beyond that, but always with the rider that the catchment area is not massive.
So there is scope for development of services at both airports and I believe that a joint owner would be a winner in this case, although I am well aware that there are those who say this never works and have quoted examples on this MB in the past.
BTW, I have no connection with BRS airport or the industry. I am a long term regular passenger who is delighted at the way pax services have improved in the south west corner of Britain in the past few years. Being greedy, I have a tremendous choice out of BRS, CWL, EXT, BHX and SOU, with LHR just along the road if I really must, but I haven't for many years now. I prefer the local airports, via hubs such as AMS for long distance travel.
Whatever happens it is an exciting time for air travel in the whole of the south west.