The best data I'm aware of that covers this is found in the Atlas of Global Christianity, which describes how Christian missions has changed over the last 100 years (1910 to 2010). An overview report of it summarizes the data:

The growth in missionary sending from the Global South is apparent in these pages but lags behind the demographics of church membership.¹

By continent, we see both the raw number of missionaries sent, as well as the number per million church members, in both 1910 and 2010:¹

                           1910                         2010
                   #Sent        #/mil.             #Sent      #/mil.
Africa               350           30             20,700         44
Asia                 300           12             47,100        135
Europe            39,950           99            132,800        237
Latin America        400            5             58,400        107
North America     20,400          223            135,000        596
Oceania              600          106              6,000        255
Total             62,000          101            400,000        184

Thus, we can clearly see that Asia, Latin America, and Africa have all jumped dramatically over the last 100 years in the raw number of sent missionaries. Asia and Latin America in particular now send much higher numbers of missionaries compared to their number of church members.

That said, the global South still lags in the latter metric, compared to the global North: North America still sends, by far, the most missionaries per church member. Still, we see evidence of a diminishing gap in that nine of the top 20 countries sending Christian missionaries are in the global South. Brazil (2), South Korea (5), and India (9) are in the top 10, and South Africa, the Philippines, Mexico, China, Colombia, and Nigeria in the next group of 10.²

The report concludes:

Over the past 100 years, as global Christianity has been shifting gradually to the South, the number of foreign missionaries sent from the South has been increasing. In 1910 the vast majority of missionaries were sent from Europe and Northern America to Asia, Africa, and Latin America. In 2010 the sending of foreign missionaries is more even across continents, although Europe and Northern America still have much higher per-capita sending rates than most countries of the Global South.¹

References:

1. "Christianity 2010: A View from the New Atlas of Global Christianity." International Bulletin of Missionary Research, Vol. 34, No. 1.
2. Atlas of Global Christianity, cited in Christianity in its Global Context, page 76.

^{Unfortunately, I have not found tradition-level data (Protestant vs. Catholic, etc.) in the sources I have.}