On the other hand, flywheels can be easily buried underground, and easily contained. The max power of a flywheel is known, so it's just a matter of putting enough concrete between humans and flywheel, a straightforward and inexpensive engineering problem. And unlike compressed air, the containment isn't under constant, wearing pressure.

You can bury the air tanks too and avoid most of the danger, but that's expensive and makes them harder to maintain. The big advantage of flywheels is that when they fail you know the energy will be discharged in a particular plane. You can orient them such that nothing vital is in that plane (like your house!). With compressed air all bets are off.

SCUBA tanks have a "burst-disk" or a weaker part of the tank that is designed to fail first, rather than the whole thing exploding and launching shrapnel. It's still violent and can throw some shrapnel, but it's much less. Also when SCUBA shops fill tanks they usually put them into a container that would somewhat contain that.

I imagine something similar could be done. It's not like there are zero safety mechanisms with compressed air.

A berm would split the difference for cost and maintenance.

Not necessarily, 1.3MJ (360 Wh; but screw that unit) of diesel isn't much of an explosive under normal circumstances. It really depends on the maximum power output under normal operation, and whether it can occur uncontrollably.

Energy density and release rate tend to have inverse relations, for a given energy mechanism.

TNT has about 1/10 the energy density of petrol or diesel. Capacitors have lower capacities than batteries.

People say that but searching youtube for exploding lithium ion batteries they seem to make fairly lame bombs. More some flames come out maybe a foot and then they burn eg https://youtu.be/SMy2_qNO2Y0?t=1m57s

I'm not sure they ever explode in a bomb like way?

Batteries don't explode in anywhere near the same fashion as an air tank, but they do include the added complication of adding a huge conflagration to the mix. So your house is burnt down instead of shattered and scattered all over the neighborhood.

360Wh of flywheel is tiny. You could easily bury it and never have to worry about the danger of a failure. Grid scale flywheels are the ones that are scary.

... and they too can be buried. Seems a bit more attractive than compressed air.

Not really. A good bomb has high velocity. Lots of high energy storage methods are slow reacting.