By your logic.. starkiller base was a big deal to the enemies of the FO... but not so much for the FO. The point is they need to have a lot on the line as well.. otherwise its no biggie for them to lose it. Then it's a tale of a man vs an ant. The ant has everything to lose, the man doesn't care what the ant does. That doesn't work the same... I mean if by taking away starkiller base and the FO just shrugs its shoulders... the rebellion isn't worth chasing around the galaxy with all your might.
In the OT, the Empire is projected to be dominate and almost unlimited in resources. The senate is just a leftover that they are finally dismissing and just getting rid of entirely (cue the Roman tie-backs). The rebellion is against the established, dominate force. So taking out the Death Star is about taking away a new capability that will further the Empire's ability to oppress and subjugate other systems. Taking out the Death Star is to knock the legs out of the empire's ability to project power and their ability to keep systems in line... not so much about 'eliminating the empire'. The death star is their new secret super weapon.. they don't want to lose as it impacts their ability to project and suppress. In V, and VII, the Empire is still assumed to be the dominate force in the galaxy with a ton of resources.
The First Order.. is not in the same spot. At the start of TFA, the First Order is itself painted as an usurper trying to rise up and gain the upper hand against the established republic. They don't have the dominance and omni-presence the Empire does in the OT.
(one of the things I don't understand about TFA is *** the 'rebels' are supposed to be fighting.. is the republic just non-military? Why are they not just the republic vs the FO?.. I actually bought the novelization this week hoping it tries to spell it out more).
So if you are this upstart... and you develop something bigger and more advanced than anything in the known galaxy.. that infers a major commitment
This isn't something they just do on the side.. It's their crown jewel. So to lose that.. is like the death star.. it seriously impacts their ability to project power and subjugate other systems. The FO is going to create a power vacuum and then try to move into it. So the starkiller base is a major tool for the FO to break out and take control of the galaxy. Losing that, hurts that plan... so this is the FO's 'skin in the game' so to speak with starkiller base.
In ESB, the empire is striking back after the rebels flee their 'no longer secret' base. ESB is a pursuit film.. the empire is seeking to counter attack and wipe out the rebels. The empire is on the offensive, they don't have anything 'at risk' in the film as they are fighting from a position of strength. The empire vs rebels then takes a back seat to the Han Solo plot, and Luke facing Vader as individuals. ESB doesn't have the same 'destroy the objective' conflict point that EP IV, VI, and VII have. So the concerns in play are different... the empire's position and strength are never in doubt in ESB.