Why did he still go after Neo? Because he is an old program. His directive was to hunt down Neo and take him down. He is working off of that directive. He also has new purpose to which is also hidden inside of Bane's psyche. Bane was jealous perhaps? Bane had hatred of Neo and the crew of the Nebuccadnezzar. There are many facets operating here. Remember, Smith wanted to join completely with Neo and Neo stopped it. So another Smith did what he did to get inside - he was able to catch Bane.