score:7
The Oxford English Dictionary has citations for the modern sense of "recession" ("A period of economic decline during which trade and industrial activity are reduced") from 1905, and from the 1840s in the more general sense of "a recession in prices".
By comparison, the modern sense of "depression" is cited as early as the 1820s ("that depression in manufactures and commerce"), with the more general "a depression in the public funds" as early as 1793. One of their citations is to an official document - by the 1880s, the UK government was appointing Royal Commissions to look into "the Depression of Trade and Industry", suggesting the term was very firmly established by then.
So it certainly seems that of the two, "depression" is the older.