From an air safety web site
JetBlue has a better records than South West
Also South West was served some fines last year for lack of maintenance.
SOUTH WEST:
1 April 2011; Southwest Airlines 737-300; flight 812; near Yuma, AZ: The airliner, with 118 passengers and a crew, was on a scheduled flight from Phoenix, AZ to Sacramento, CA, when it experienced a rapid loss of cabin pressure after a rupture developed in the upper fuselage about 18 minutes after takeoff when the aircraft was climbing through 34,000 feet. After the loss of cabin pressure, the crew was able to divert to Yuma, AZ without further incident. There were no serious injuries among the 118 passengers and crew members on board. The rupture was about five feet long and about a foot wide
19 April 2010; Southwest Airlines 737-700; flight 649; Burbank, CA: The airliner, with 119 passgengers and a crew of five on board, nearly collided with a Cessna 172 at Burbank Airport in California. Flight 649 was inbound from Oakland to the Burbank airport (also known as Bob Hope Airport) and was landing to the east on runway 8 while the Cessna 172 had just taken off to the south from runway 15, passing over the 737 at the intersection of the two runways. The two aircraft came within 200 feet vertically and 10 feet laterally of each other at the runway intersection. At the time of the event, skies were clear with 10 miles of visibility. No one on either aircraft was injured and neither aircraft was damaged
8 December 2005; Southwest Airlines 737-700; Chicago, IL: The aircraft was on a scheduled flight from Baltimore to Chicago's Midway Airport. After landing, the crew was unable to stop the aircraft on the runway, going off the runway, through the airport's barrier fence and onto a nearby street. At some point during this event, the nose wheel collapsed. The aircraft struck at least two vehicles, with the impact causing fatal injuries to a six year old boy who was a passenger in one of the vehicles. None of the five crew members or 95 passengers were seriously injured. This was the first serious accident involving the 737-700
11 August 2000; Southwest Airlines 737; en route from Las Vegas, NV to Salt Lake City,
UT: The aircraft was on a scheduled flight from Las Vegas to Salt Lake City when about 20 minutes before landing, a 19 year old passenger became belligerent and attempted to enter the cockpit. While being escorted back to his seat, the 19 year old attacked another passenger. A number of other passengers subdued him until the aircraft landed. After landing, the now unconscious passenger was removed from the aircraft and he died several hours later. The medical examiner found traces of drugs in the dead passenger's system, but listed the cause of death as suffocation. The death was classified as a homicide, but none of the passengers involved in the incident were charged with a crime. No other crew members or passengers were seriously injured or killed
JETBLUE
21 September 2005; JetBlue Airways A320-200; Los Angeles, CA:
Shortly after takeoff on a domestic scheduled flight from Burbank, CA to New York, the crew became aware of a problem with the front landing gear. The wheels on the landing gear were locked in an incorrect position, leading the crew to divert to Los Angeles for an emergency landing. The landing, broadcast live by CNN and many other television networks, was visually spectacular but did not result in any serious damage to the aircraft. There were no injuries among the 140 passengers and six crew members.