The Space Shuttle was a far less reliable system from a fundamental design perspective. The size of the wings, the nature of the thermal protection system, the insulating foam and the use of a super-cryogen as fuel, the side-by-side staging, the use of solid fueled boosters on a manned launcher, etc. Engineering estimates show that we were incredibly, incredibly lucky to have the Shuttle safety record we did, the vehicle was a death-trap. We almost lost Atlantis in 1988 and Discovery in 2005 to the same thing we lost Columbia to, and we almost lost several shuttles in the early 80s to the same fate that doomed Challenger.

Of course if an organization ever gets complacent about safety then things can go downhill, but in the case of SpaceX they have a fundamentally more robust vehicle design, a system with more and safer abort scenarios, and every possible reason to maintain a high degree of vigilance about safety (if for no other reason than their company's image and financial bottom line).