[thetwiceler]

Firstly, Kalman filtering is optimal, that is, it produces exactly the correct posterior distribution. As you mention, particle filters cannot achieve this.

It's a rough heuristic that to achieve a certain accuracy for a linear/Gaussian system with a particle filter, you need a number of particles exponential in the number of dimensions of the system. I feel like this could probably be stated more formally and shown, but I don't think I've seen anything in that vein. The Kalman filter, being simply matrix operations, should scale as the number of dimensions cubed.

So yes, Kalman filtering is computationally more efficient, and (obviously) more accurate.

I also wouldn't discount the fact that the Kalman filter is, in a sense, simpler than the particle filter for a linear/Gaussian system; you don't need to worry about resampling or setting a good number of particles, and you don't need to compute estimates of the mean/covariance statistics (which are sufficient since the posterior should be a Gaussian).

[RogerL]

Under the same conditions of linearity and Gaussian noise you can get essentially optimal performance. Of course, why would you when the KF is so much more efficient.

[papaf]

This is true but the assumption of Gaussian noise carries with it the assumption that the model is correct.

Most models are not correct which is why particle filters perform much better than people expect.

[donquichotte]

Particle filters can be an option if the noise is not additive (e.g. scales with signal amplitude) and Gaussian.