wow, what a coincidence that they sound so similar. wiktionary says the english "better" is "...from Proto-Indo-European bʰed-rós, from bʰed- (“good”). Cognate with Sanskrit भद्र (bhadrá, “blessed, fortunate, happy, good”)"
nothing about बेहतर though, which it says is from Persian بهتر (behtar) but doesn't give further etymology.
I'm no expert but it seems to be just a remarkable coincidence. Persian behtar in the comparative of beh, an archaic word for good, which comes from a different PIE root, hwesus. In fact the similarity of the Persian comparative -tar and the Germanic -er is just luck too, since in Proto-Germanic it was -izo and has since been rhotacized. (Interestingly it looks like Gothic had two words for "better": iusiza from PIE hwesus (possibly) and batiza from PIE bhed. That would make behtar cognate with the former, despite looking more like the latter!)