It should be safer than the Shuttle (STS).
I don’t think anyone, even today, really knows how reliable the STS was. Before the Challenger disaster, NASA management had wildly optimistic views on STS reliability: 1 failure in 10,000 launches, for example. That was obviously not true. Based on how it actually behaved, a 1-2% failure rate is more likely.
The Falcon 9 has had 87 launches, 85 full successes, and one partial success (primary payload was placed in orbit). Very roughly speaking, that is on par with the STS failure rate.
However, the STS had few realistic abort options. Although they planned a number of contingencies, some of these sound like a joke–for example, if they can get the Shuttle into a stable glide over the ocean, they can extend a pole from the door and slide out, parachuting to safety. But the odds that a launch anomaly can result in the Shuttle flying away without significant damage seem negligible to me.
In contrast, the SpaceX capsule (like all capsules) has a launch abort system that can pull the capsule away from the booster. It has a heat shield on the bottom, adding some protection, and is basically a simple system that can work under a wide variety of situations (including an exploding rocket). The capsule would have been just fine in the one Falcon 9 full failure.
Unlike other capsules, the Dragon keeps its abort system all the way into orbit. Most use solid rocket motors that are jettisoned sometime during flight, and so lack a working abort during that time. Dragon can abort for the entire launch.
So while the launchers are probably comparable in reliability (though I’d still give the nod to SpaceX), the chance of launch of life should be significantly lower for SpaceX. NASA gives the odds at 1/270 (or at least that was the standard they had to hit).