Multiple sources agree that Conoclinium dissectum and Conoclinium greggii are synonymous: Flora of North America, The Plant List, USDA PLANTS Database, Flora Neomexicana III, ITIS, etc. I don't know of anyone who considers these separate species.

Where there is disagreement is on which name to use. I am not sure of the source of this disagreement, but it's really not a matter of which flora we want to follow, it's a matter of following ICNafp. Conoclinium dissectum was published in 1852:

http://www.ipni.org/ipni/idPlantNameSearch.do?id=197046-1

Eupatorium greggii was published in 1884:

http://www.ipni.org/ipni/idPlantNameSearch.do?id=206009-1

Then moved to the genus Conoclinium in 1902:

http://www.ipni.org/ipni/idPlantNameSearch.do?id=64241-2

Assuming we consider the two to be synonyms, which all sources do, the correct name is the one published earlier:

"11.4. For any taxon below the rank of genus, the correct name is the combination of the final epithet1 of the earliest legitimate name of the taxon in the same rank, with the correct name of the genus or species to which it is assigned, except (a) in cases of limitation of priority under Art. 14, 15, 56, or 57, or (b) if the resulting combination could not be validly published under Art. 32.1(c) or would be illegitimate under Art. 53, or (c) if Art. 11.7, 22.1 or 26.1 rules that a different combination be used."

http://www.iapt-taxon.org/nomen/main.php?page=art11

Clicking through the exceptions is kind of fun, and I encourage doing so, but none of them apply in this case.