I do think they need to be separated in any case, until it's firmly proven that they are--and were originally--the same rose. At this point, it seems to me that they were lookalikes rather than true synonyms. The writer, Mr. Falconer, clearly knows Burgess, and his statement has an air of knowing personally that 'Mrs. Degraw/Degrauw' has been around a long time (rather than trusting Burgess on that). A lot depends on what "many years ago" in the quote means; to me, that implies a decade or more. One of the parents of 'Champion of the World' is understood to have been 'Magna Charta', which was introduced in 1876--in England. If the implication is that 'Magna Charta' was a parent of 'Mrs. Degraw', that really doesn't leave "many years" for 'Magna Charta' to be imported to America, propagated and sold, grown in Glen Cove, to have had crops of seedlings, for the crops of seedlings to themselves grow and be assessed, and for one of them to be found worthy and had any sort of distribution, even locally--everything would have had to have been on the fast track, which doesn't happen very often in Horticulture. But meantime, I'm investigating further.

If it and 'Champion of the World' are the very same rose, then the name with priority through chronological precedence is 'Mrs. Degraw' (or 'Mrs. Degrauw').

Here we go: “At the present time the ‘voice of the birds’ is whispering that ‘Mrs. Degraw’ and ‘Champion of the World’ are possibly identical with, or very similar to, that good old Bourbon, ‘Pierre de St. Cyr’. [As grown alongside of each other by V.H. Hallock & Sons, of Queens, N.Y., and critically compared at different times by leading New York rosarians ‘Mrs. Degraw’ and ‘Champion of the World’ have been pronounced distinct. Ed.]” Gardening, vol. 1, May 1, 1893, p. 260.

They should be separated. Now the question is "Degraw" or "Degrauw"?