Crowley and Aziraphale ultimately wanted the same thing:
To live happily and peacefully together on earth, free from the looming threat of heaven and hell.
Crowley's solution was to run away together. If they got far enough, they'd be out of heaven and hell's reach and could simply be an 'us'. After all, it worked for Beelzebub & Gabriel right?
Except Aziraphale correctly recognised the flaw in that plan. It worked for Beelzebub & Gabriel because those two didn't care about humanity or earth, only each other. Crowley (and Aziraphale) on the other hand, very much do. Running away would ultimately fail because they could never truly be happy leaving humanity to their (predestined, doomed) fate.
Aziraphale's solution was to 'fix' the system. If he tried hard enough he could course-correct heaven, un-doom humanity, and 'then' they could be together. With enough love and kindness, everything would eventualy work out the 'right way' surely?
Except Crowley correctly recognised the flaw in that plan. Heaven and Hell were fundamently broken, or rather, working exactly as intended. No matter how much Aziraphale (or Crowley) wanted or tried to influence the higher powers and their plans, it would only ever be temporary, and they'd never truly be at peace. Trying to change things would ultimately fail becuse the ineffable plan decreed an end-times.
It's the tragedy of their story. They were working at odds to each other to achieve the same end, with both of them doomed to fail, but only able (willing?) to see the hopelessness in each other's plan. It was only at the very end that they saw that what they wanted was never truly possible in their current universe.
So instead they chose a new solution, together.
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