Are there sources for both of these practices? What reasons do the sources give for doing this one way or the other?
It seems to be a machlokes.The sefer Ishei Yisroel pg 259 brings many shittos about this. I will mention some, the rest see inside. He brings the Biur Halacha 125 seif 1 at the end of elah,he writes that if the chazzan starts after the congregation it could be that it would be considered saying kedusha b'yichidus.He brings the Pininim v Igros Zev who brings from the Griz M'brisk that was m'dayik from the Ramabam's loshon in seder tefillah that when things are said together with the congregation "he should say it with them." He adds that a minyan which is exactly 10 and the chazzan doesn't answer with them even for the congregation it is like they said it b'yichidus.
On the other side,there are shittos who hold that the chazzan says it after the congregation. The bais Yehuda(shu"t)chelek 2 siman 3 writes that it is ok for the chazzan to answer after since his intention is to be motzei the congregation just like the rest of chazaras hashatz which he says alone. See also the Igros Moshe OC 3:4 that he starts after the congragation.
There are alot of sources so see it inside if your able to.