Which Power Management implementation to use and the differences therein

In general, a single boost circuit is preferable to using two boosters in series. I say this because, given the powers you require, a transformer is the most efficient way to do the step-up from 12V to 400V.

Not using a transformer will limit the power you can handle in stepping up the voltage. At these sorts of power levels you'd be hard-pushed to find a booster that doesn't use one. Once it is accepted that a transformer is a requirement, any turns ratio from a 100:1 (step-down) to 1:100 (step-up) is just a matter-of-fact (see comment below next paragraph).

Because a transformer is necessary to economically achieve the power output, the turns ratio is going to be an easily achievable 40:1. A 24Vp-p input at a frequency of (say) 10kHz will, under no-load conditions, produce an output of 960Vp-p which after rectification/smoothing is going to be about 475VDC.

But, high turns ratios and efficiencies don't always go hand-in-hand - I'm thinking of X-ray tube power supplies that I've used - they were 50KV/4mA output (200W). The step-up transformer was a large ferrite operating at 50kHz and, with about 1200 turns on the secondary you were starting to hit self-resonance. It was a resonant transformer circuit so that was no problem but more than 1200 turns and you were on the downward slope of decreasing efficiency. Input turns, from memory were about 6 so turns-ratio of about 1:200. The output fed a multi-stage cockcroft-walton voltage multiplier to take the output up from about 2000Vrms to 50kV.

More than likely (given the power), you'll need a H-bridge driver which will apply nearly 24Vp-p to your primary winding and the turns ratio will be 40:1 to produce +400VDC. It will need a reasonably sophisticated control system that involves pulse width modulating the drive to the primary and decent monitoring of the output to ensure you stay regulated. I would also say that a secondary shut-down circuit would be needed should a single-fault arise. Caution - fire hazard, electric shock hazard

Given the power supply's sophistication I'd be very hesitant to believe that two boosters would be at all more effective than one booster on the grounds of efficiency, performance, physical size or cost.

There are two problems with your idea. One practical, and one fundamental.

The practical problem is that per amount of stored energy capacitors are more expensive than inductors, and on top of that the realy high-capacity capacitors (electrolytic) age.

The fundamental problem is that charging a capacitor from a voltage source is fundamentally lossy (you dissipate heat). This might seem counter-intuitive, but is nonetheless true. (There was a question about this some time ago.) Hence a flying-capacitor voltage converter, even an ideal one, is inherently inefficient. (An ideal inductor-based voltage converter is 100% efficient.)

You might think it strange that the world is unfair to capacitors, but that is our human fault: we supply power mostly from voltage sources. For current sources the inverse is true: an ideal current converter from flying capacitors can be 100% efficient, while one from inductors must necessarily be lossy.