Of the recent rivalries, it still has to have history (though recent), fervent fan bases, and major encounters. The Red Sox-Yankees rivalry was one sided, but it was still a rivalry (competitive balance and give and take makes it more intriguing but it’s not a necessity for a rivalry). Players can take rivalries with them (CP3 and the Warriors; Kyrie and the Celtics).
Kyrie’s history (all the way to stepping on Lucky and comparing the fan base to a scorned girlfriend) amps the Celtics-Nets rivalry, but they lack the fervent fan base; for me, it’s a step below the Sixers. I dislike losing to those guys more than any other team in the league.
The Heat-Bucks rivalry is one of the best rivalries in the NBA today. They’ve faced and eliminated one another in back to back seasons, cherry picked key players, and talked trash to each other.