I cannot speak on a comparative economic level as North Korea, but Cuba suffered hard with the fall of the Soviet Union. Much of Cuban trade and aid had been with the USSR. They had to rework most of their economic system in order to survive. The time from the fall of the Soviet Union to about 1995 is known as the "Special Period" which was notable for a number of economic changes in the country.
Opening to foreign investment
Allowing some Private Enterprise
Promoting tourism
Each of these tactics was used by the Cuban government as a means of bringing hard currency into the country, and to keep the government operating on its socialist system. Though it became more difficult, healthcare, education, and its food system were still key revolutionary advances promoted by the government. In the case of private enterprise, it was possible to create and operate your own business, but with heavy taxation and fines, this incidentally lead to further increase in tourism as Cubans opened their own restaurants and opened their rooms to rent to visitors and tourists as well as an increase in farmers markets and other bodega style stores. In 1993, Cuba also legalized the use of the American dollar as a means of increasing both trade within and without in the country. Another means of economic reform that some might find interesting is the use of two forms of paper currency in the country, the CUC or Cuban Convertible peso, and the Cuban peso, the CUC has a placed value equal to the dollar and is what the tourist and businessman uses, while the cuban citizen uses the regular peso, to the point that they will work to keep the regular peso out of the hands of the tourist. Since then special period, Cuba has slowly allowed more capitalist ideals to work themselves into the country but at heavy taxation and under intense scrutiny. A small business owner can be shut down at any point and his business license revoked.
If you must look at them comparatively, it is obvious that Cuba has survived the fall of the USSR much more gracefully than North Korea has.
Sources: A History of the Cuban Revolution, Aviva Chomsky, A History of Latin America Keen and Haynes
EDIT: To add some additional information, there isn't a personalized Juche style of Socialism/Communism in Cuba due to Castro's desire to keep away from having a Cult of Personality. In terms of the negative things happening after the fall of the USSR, there is a sharp rise in crime such as prostitution, begging and drug running but nothing like the mass starvation and repression seen in North Korea.