In The Prestige, Angier and Borden's rivalry seems to be inspired by The War of the Currents. Are there any parallels between the characters of Angier and Borden with Edison and Tesla?
This has been touched on a little in the answers to this related question already.
While it's maybe not so much that the Angier/Borden rivalry was "inspired" by the Edison/Tesla rivalry rather than being used as an emphasizing backdrop, we can indeed draw a few quick analogies between those two chracters and those historical figures.
If we take Borden and his dedication to his art, we see that he primarily does his magic for art's sake and to master his craft. This comes together with less of a practical consciousness about the needs for actually performing and selling his magic, or as Cutter puts it:
Cutter: He's a wonderful magician. He's a dreadful showman. He doesn't dress it up.
Compare this to Nikola Tesla who was an incredibly creative mind inventing all kinds of things, but ultimately not making much commercial success from it. He didn't sell much of his stuff but also didn't seem to have much interest to do so, rather than advancing our understanding of science. This similarity between the two is also reinforced by Christopher Nolan drawing that comparison in a making-off about the movie:
For me the relationship between Borden and Tesla is interesting because they're both people who can see beyond and can see things beyond everyday reality and understand effortlessly the world they've devoted their intellect to, but don't perhaps understand the best way to sell it, don't deal with the political, practical realities, how you channel that talent.
You can then contrast this with Angier, who always tried to trump Borden and be more successful than him. But for him it was always more about fame and actually impressing the audience. He did care more for discovering Borden's secret and having more success than about developing his own trick to leave his mark. He usually tried to go the quick and dirty way than devoting his entire non-stage life to his art in the way Borden did. But he also knew much better how to sell his magic, he ultimately was a performer and an actor.
Angier: No one cares about the man who disappears. They care about the one who comes out.
Angier: I don't care about my wife. I care about his secret.
Now set this in relation to Edison, who was much more of a businessman than Tesla and made much more real-world success than him, even if sometimes through rather aggressive or dubious business tactics.
We might even want to draw a more judging comparison between those 4. While neither Borden nor Angier stayed entirely clean during their rivalry and there's maybe not an actual winner, seeing how much they both sacrificed, the film ultimately seems to put Borden as the moral winner of the story (even if only by a slight margin). In the same way, modern history has put a more differentiated view on Thomas Edison and his sometimes not always entirely fair business practices, especially in relation to the injustly forgotten Tesla.