H₂S acts only as a reducing agent while SO₂ can act both as a reducing and oxidizing agent because 

H₂S, the oxidation state of S is — 2. So it cannot accept more electrons because on accepting 2 electrons S acquires a noble gas configuration. So, it can acts only as a reducing agent by loosing electron. On the other hand, the oxidation state of S in SO₂, is + 4 which is an intermediate oxidation state of sulphur so it can reduce as well oxidise.