I'm by no means an expert on solid rocket motors, but it's my understanding that, although they may fail suddenly, they don't necessarily do so without warning. It may be possible to sense a imminent failure and actuate the emergency escape system before a catastrophe occurs. It is also my understanding that once a solid motor casing ruptures and the pressure is relieved, the motor essentially shuts down. On the other hand, liquids propellants can ignite into a massive fire ball upon engine failure. Again, I don't have any personal experience with this, this is just what I've read.
There may be signs of imminent failure, and there may not be. A fragment breaking loose and sharply increasing the surface area or blocking the central channel or a casing failure will cause a very sudden explosion.
Burn rate may drop steeply, but it doesn't stop burning. There's been quite a few failures that resulted in a spectacular shower of flaming chunks of fuel. This was one of the objections to Ares I, at some points during launch a failure would lead to the capsule's parachutes opening in the debris pattern, with essentially zero chance of surviving due to heating from the burning fuel around it.
Liquid engines are far more likely to shut down cleanly, and don't need to be blown up in the process. The Falcon 9 can even continue on its mission after experiencing an engine outage, as the Saturn V was capable of, something that is simply impossible with solids. If there
is a catastrophic failure, the fireball is far more localized due to the fuel consisting of fluids that rapidly disperse...no large footprint of flaming debris. The fuel is also poorly mixed, and will not burn all at once or even completely.
Liquid engines can also be tested prior to launch, or abort without leaving the pad. The recent SpaceX Dragon flight shut down on the pad moments after starting up due to abnormal pressure readings from one engine. After changing a valve, they launched and did a successful mission to the ISS. If it had used solids, the vehicle would have been lost either due to immediate explosion or by self destruction by the range safety systems. In a manned vehicle, you'd be comparing a similar delay with the crew arriving days late, to a failure with the crew violently being blasted away from an exploding vehicle via emergency rockets and hopefully clearing the debris pattern.
Solid propellants also have a high density impulse, meaning high impulse per unit volume.
Not hugely more so than LOX/RP-1, except at the smallest scales.
The high thrust of solid motors can be used to offset much of their ISP disadvantage. For instance, if a solid fueled booster has a higher thrust-to-weight at liftoff than a liquid fueled booster, then less of the thrust is used to overcome gravity. Say, for example, that a liquid fueled booster has a T/W ratio of 1.25 at liftoff, then 80% of the thrust is used simply to cancel the pull of Earth gravity. Using a more powerful solid booster we might be able to increase the T/W ratio to, say, 1.5. In this case only 67% of the thrust is canceling Earth's gravity. This can make the solid fueled booster effectively more efficient than the liquid fueled booster despite the fact it has a lower ISP.
This only applies briefly, while the vehicle is initially accelerating vertically, and requires accepting the safety issues and limitations, environmental issues, etc of solid rockets. And even as strap-on boosters, in real world rockets they have proven to be lower performance than liquids...liquid boosters were considered as a way of increasing the payload and safety of the Shuttle.
They are simple in concept, but complex and hazardous to fabricate and handle, inflexible in adapting to different missions, and do not scale up well...note the several tons of tuned mass vibration dampers that Ares I needed to keep from killing its crew or shaking itself apart. Solids aren't nearly as simple and cheap as they're advertised to be.
