Even as late as 1920, the Atlantic Ocean could be dangerous.

In the year 1920, 356 ships were lost in the Atlantic Ocean (some were not lost permanently, as they were later re-floated after having run aground, or salvaged)

In 66 of these 356 maritime incidents there was loss of life.

More than 1017 people died in these maritime disasters in 1920. (Crew, passengers and rescuers). (1017 fatalities are cited. In addition, 21 of the ships were lost with all hands but the number of hands was unknown).

Ships were lost by foundering, collision, fire, running aground, unknown causes, and 9 were sunk by naval mines (obviously still a problem in 1920 from mines left over from WWI, mostly in the North Sea).

Of these ships, 142 were sailing ships, 200 were powered cargo or fishing ships, 15 were naval ships, and 9 were passenger ships.

Of the 9 passenger ships, only two were lost with any loss of life. (2 caught fire in harbor with no passengers on board, 5 ran aground but either evacuated the passengers and crew or re-floated the ship.)

Of the two passenger ships lost with fatalities, One was the Swedish liner "Jemtland", which hit a mine and sank in the Baltic. She had no passengers on board at the time, but 5 of her crew of 26 were lost.

The worst passenger liner disaster that year was the French Ocean liner "Afrique", which foundered in the Bay of Biscay with 599 passengers and crew on board. 556 were lost. Only 43 were rescued by the French ship "Ceylan".

However, in 1920 430,000 immigrants arrived in the USA (not all of them by crossing the Atlantic Ocean, but most of them), and there were many travelers on Atlantic ships who were not immigrating to the USA.

If we roughly estimate 300,000 to 500,000 passengers traveling on the Atlantic in 1920, the circa 500 passengers who died that year on the "Afrique" was not a very high percentage, so being a passenger on an Atlantic voyage was probably fairly safe and not very scary (unless you were unlucky).

Sources:

http://en.wikipedia.org/wiki/List_of_shipwrecks_in_1920

https://www.google.com/search?q=immigration+statistics+1920s&tbm=isch&tbo=u&source=univ&sa=X&ei=JlmCU6ewDcuPyASgr4KIBA&ved=0CDYQsAQ&biw=807&bih=504#facrc=_&imgdii=AvcCBFeuMY1n0M%3A%3Bq1B_HphM0SCcIM%3BAvcCBFeuMY1n0M%3A&imgrc=AvcCBFeuMY1n0M%253A%3BDUwiBbkt4wl0bM%3Bhttp%253A%252F%252Fpages.ramapo.edu%252Ftheed%252FMLS%252520610%252520Multiethnic%252Fimages%252Fg%252520Mar%2525207%252520Eastern%252520Europeans%252Fimmigration-1870-1920.jpg%3Bhttp%253A%252F%252Fpages.ramapo.edu%252Ftheed%252FMLS%252520610%252520Multiethnic%252Fsessions%252Fg%252520Mar%2525207%252520Eastern%252520Europeans%252FMar%2525207%252520Eastern%252520Europeans.html%3B668%3B580

Time of year was also quite important, as the north Atlantic and it's icebergs were and continue to be a constant danger. The warmer months going toward South America also expose ships to tropical storms and hurricanes.