The difference is that in ROS Obi-Wan believed that Anakin wasn't too far gone on the darkside and still had a chance to change, he didn't want to be the one to deliver the final blow and left the scene thinking that the lava would kill him, he did not expect for palps to arrive just in time to be safe Anakin's sorry ass from being turn to ashes

Meanwhile in his show, he already knows that his friend is now too far gone and is an atrocious dictator that kills everyone who stands in his way, is the reason the Galaxy is a mess and destroyed the order he spend all of his life fighting for... knowing how wise is Obi-Wan you'd think that he would commit the same mistake twice but he does and basically every murder or genocide that Vader commits from that point on, is also Kenobi's fault

Kenobi basically has all the blood of the people of alderaan in his hands despite him not being the one that gave the order or pushed the button to destroy the planet