The difference between the 2 diodes might become evident when used in the intended applications.
This means Switch Mode Power Supplies, power inverters (= SMPS) and high power motor controls where high reverse current peaks need limiting to protect the switching devices from a premature death due to extremely high reverse voltages generated by the inductors/motors/transformers when the current is switched off (10,000 to 100,000 times per second).
That is where these special diodes are designed for, it cannot be done with 'normal diodes'.
Interchanging these diodes
may reveal slight differences in RF emission from this kind of equipment or have influence of the efficiency (thus heat emission).
You wouldn't be able to use them in those applications anymore when you would fit even 100pF across them though.
For rectifying mains they are both kind of overkill and add nothing, as explained earlier the difference in nanoseconds is negliable small compared to the actual time in ns the diodes are conducting in 50/60Hz rectifiers.
The MUR420 has the edge in forward voltage drop (around 0.15V lower at around 0.5A) over the C3D06065A
The C3D06065A can handle slightly more current though.
The snubbers across the diodes serve 2 purposes both of which are HF (emission) related.
For the DC voltage on the reservoir caps they have no influence.
Effectively what the capacitors do is 'short' any spurious HF entering FROM the trafo as well as 'snubber' which is kind of 'smoothing the transition point' the diodes.
Relatively spoken the voltage change (at the switching point) is so enormously small (in the mentioned ns) that the diodes (even the slow ones) have no trouble keeping up with it.
HF garbage from the mains is not coming through a trafo by inductance but comes from capacitive coupling of the primary and secondary windings.
Toroids are worst in that aspect followed by E-core and R core has the least HF coupling (in both directions).
Also there are VERY small HF peaks on the secondary side of the trafo (couldn't see them on the scope but sensitive RFI receivers may pick up very low level RF) at the moment the diodes start and stop conducting.
They conduct only a fraction of the time (when the sinewave of the trafo reaches the voltage that is in the reservoir caps) and the rest of the time they are in 'reverse' and do not conduct.
anyway... the capacitors effectively form a 'short' for HF signals (above 1MHz) between the 2 secondary windings as well as between the + and - of the reservoir cap.
effectively almost the same mounting a 5nF cap across the secondary windings and one 5nF over the reservoir cap.
There is a difference though as it also prevents the diodes from emitting 'switching' artifacts, which are extremely low amplitude and high in frequency in this case anyway (when not snubbered).
So if your reservoir cap already has a 10nF (or even 100nF) decoupling cap across it already you can omit the 10nF but for these low frequencies (100Hz sinewave and perhaps) removing those caps will go unnoticed.
No reason to take the 10nF caps out though, but mounting a very fast diode and making it extremely sluggish again defeats any profit that can be had 'speed' wise from the diodes.
The differences in forward voltage also aren't very shocking.
You must realise the diodes only 'connect' the mains (via the trafo) around 1ms every 20ms the rest of the time it is 'off' and mains is litterally disconnected by the diodes.
So the general idea in hifi land that audio currents come directly from mains at all time is hereby declared nonsense as well as most of the time (90 to 95%) the mains aren't even supplying the power at all... the reservoir caps do and get charged every 10ms (or 20ms) for a short period of time.
Only for HF garbage there is a continuos connecting with mains when snubber diodes are fitted, but at the same time is 'shorted'.
So technically the change of diodes (certainly with snubber caps) made no technical difference in THIS application except for the slight loss of voltage on the reservoir caps.
When regulators are used (in most cases) this would go unnoticed.
???How removing the caps and changing the diodes alters the PERCEPTION of the music is an entirely different matter and is not technically explainable by the speed or other technical factors (that are known to the technical people).
PS I know I am completely ignoring the thousands of reported improvements that appear to prove me wrong.
I don't mind I am free to speak my mind (I hope) and if people clearly hear differences than at least to them it is a very worthwhile upgrade.
I am completely O.K. with that b.t.w.