Hey Gerry,
Actually, I like Priest, and I agree there is a lot of processing in those two examples, but I don't feel it's over processed. It's actually very tastefully done IMHO, and here is why I think so:
I can hear the guitars are heavily chorused, but the effect is on the guitar amps, not on the tracks. Now here is something I learned in a studio back in the 80's, when using a thick, or heavy chorus effect to essentially double the sound it's added to, there are two ways to do it. One way is time shift modulation, the other is pitch shift modulation. If you want to combine Chorus and Reverb without it getting muddy, then the best way is to use pitch shift modulation for the Chorus, because Reverb involves time shifting. This way, the time shifts do not clash with each other.
This is also true when two guitars are chorused. I believe I am hearing this on the 1st link. The guitars are heavily Chorused with no Reverb, but both are very distinct. I hear the Reverb applied to the Vocals, and to the Drums. The Vocals have a Hall Reverb while the Drums have a rich Plate Reverb that is placed after the Compression and EQ effects, and I believe I am picking up a very short Delay on the Snare Drum, almost inaudible.
In all, I believe this is how you can use heavy processing, yet still keep it sounding like a live band, just with an enhanced sound.
@MJMP, Yes, there is a lot of processing on that album, but like the above, it's not so much that it works against the band. It actually makes the band sound more exciting.
Just my humble opinion according to my personal tastes.