In terms of total population, the 1884 $3 is the rarest of all the dates in the 1880's. However, it is not the most difficult to obtain in Mint State -- that distinction belongs to the 1881. The 1884 appears most often in MS63, but there are a fair number of MS64's and a few Gems, as well. Top examples include two PCGS MS66's (one from the Great Lakes Collection and another from the South Texas Collection) and some NGC MS67's.
The 1884 $3 is an extremely popular date because of its very small mintage.
Great Lakes Collection
American Princess Collection of $3 Gold - Heritage 4/2009:2696, $46,000