Not really (and incidentally the 'to him' would normally follow the verb). In fact you could use the object pronoun as a distinguishing feature in this pair:
- She said to him that she was sorry.
- She told him that she was sorry
It is true, though, that after 'said' you can omit the 'to him'; if, however, you omit the indirect pronoun after 'tell' you are left with an admittedly not uncommon but nonetheless very basic mistake.