There are a number of key differences between the first and second tablets:
The Tablets themselves: The first tablets were ''the work of God'' [Ki Tisa 32:16], whereas the second tablets God told Moshe to ''carve for yourself'' [34:1]
The writing: The Talmud states that only the first tablets possessed the quality of ''God's writing'', which would have caused the words to be forever engraved in Israel's heart and never forgotten [Eruvan 54a and Rashi ibid]
The spiritual level of Israel: By the first tablets, the Jewish people were tzadikim [saintly], whereas by the second tablets they were ba'alei teshuvah [penitents].
The spiritual level of Moshe: Moshe was given ''one thousand lights'' as a present when the Torah was given, but with the sin of the golden calf they were taken away.
The second tablets had the advantage that (a) they were given with ''halachot, midrash and aggadot'' and (b) Moshe's face shone with light when they were given.
Source: Lubavitcher Rebbe Hayom Yom 17 Tamuz