Not really the same comparison. Clark is an absolute nobody. And he has no real reason to hide his face when he hides so well as Clark Kent. Clark is in fact his mask. While with Batman, Bruce Wayne is a public persona. He's known throughout the DC universe. Like we learned with The Dark Knight people begin to connect the dots and trace it back to him. The voice modulator helps conceal his Bruce Wayne voice and make that just a bit harder. Especially when he's around people who probably know Bruce Wayne.

For all we know Bruce has figured it out. The way he looked at Clark as he said his "freaks dressed like clowns" line. Up and down implying he knew. As for the people in Smallville I'd like to think a lot of people know and just choose to keep quiet. Like Lana Lang and Pete Ross. Pete Ross saw what his mother became when she heard what Clark could do. He kept quiet until Lois figured it out. And even then he only pointed her to the Kent house, not outright throwing Clark under the bus. Pun intended. He knows Clark is pure hearted and just wants to help. Unlike everyone else who worships him or condemns him.