The Weber Copper Cap contains couple of diodes, a couple of power resistors to simulated the impedance of the rectifier, and a thermistor to limit in rush current.
My experience with them is that they do a very good job, although the 5Y3 version drops more volts than most real 5Y3GBs.
Even with the in rush current limiter, the Copper Cap will turn on faster than a valve rectifier.
The impedance of valve rectifier, being used sensibly, is more or less linear, so an appropriately sized power resistor after a solid state rectifier causes the power supply to sag in a very similar fashion.