Are generation 3 nuclear plants safe?

Most nuclear power plants are quite safe. The only ones that were inherently unsafe ware the Soviet-made power stations similar to Chernobyl, which did not include a reactor containment building.

The nuclear powerplant at Fukushima Daichi in Japan was crippled not by a failure of the nuclear reactor, but by the tsunami following the magnitude 9+ earthquake. The plant survived the earthquake, and the plant operators shut down the reactor, but a nuclear reactor generates a LOT of heat, and takes a while to cool off. When the reactor isn't providing power to run the coolant pumps, external power must be supplied to run the pumps to cool the reactor. Fukushima Daichi had backup diesel generators for this purpose, and power from the electrical grid as a backup - but the tsunami knocked out the generators and knocked down the power grid all along the coastline.

The new reactor designs are not susceptible to failure when the coolant pumps go offline.