All of the top brass at T3 hate BE, with a passion, hell would freeze over before RL would sell his baby.
The 2 airlines have nothing in common, different fleets, different markets and one makes money the other does not, unless supported by a bigger player.
E.G If it was a friday night and Flybe had 3 pax travelling from SOU / LBA would it operate, not a chance
Where as Eastern would, that is why business travellers choose Eastern ahead of BE. they will find you a way home even if they have to choose another route to drop in to another airport on the way