Ras al Ghul's issues with Batman have been pretty consistent since they first met face to face. He wants Batman to take over his role, continue his line through Talia, and if Bat's won't, he's simply too likely to thwart Ras' goals to risk leaving alive.
On the other hand, Luthor's gripes with Superman have undergone some kind of change with every reboot.
These examples provoke two questions from me:
- What are some of the long-running archenemy pairings whose dynamics have changed, and was that for better or worse?
- Alternatively, what are some of the long-running animosities that have stayed the same, and what's given them that staying power?