A few months ago I sent 6 ICCS-graded coins (plus one raw coin) to PCGS, first time trying to cross any graded coins whatsoever. They were all older (silver-era) Elizabeth II pieces. I've seen a few threads on this topic in the past but I figured I would share some more results for those who are interested, since I just got them back now.
Firstly, I sent the first coin I ever bought at an LCS, both because it's a nice coin and has sentimental value for getting me into the hobby. My 1966 25c came back MS65, which is a great grade, although that doesn't tell us much about the topic.
Anyway, here are the actual results of the 6 crossed coins:
1962 1c: PCGS MS64RD (ICCS MS65RD) -- notably, ICCS recognized the "Missing M" variety, PCGS does not.
1953 10c, SF: PCGS MS65 (ICCS MS65)
1956 50c: PCGS MS63 (ICCS MS65)
1956 $1: PCGS PL66 (ICCS PL66)
1953 $1, NSF, FWL: PCGS MS64 (ICCS MS65)
Finally, the one I'm most proud of:

1953 $1, NSF, SWL: PCGS MS65 (ICCS MS65)
Notably, the ICCS holder didn't recognize either the FWL or SWL varieties here, only the NSF on the obverse. PCGS does, but only now. They didn't previously differentiate, which is annoying for the pop reports they maintain. It leads to a funny result when opening the coin in the PCGS app:

They clearly have some sort of algorithm that guesses the value of the coin based on the grade and population--reminds me of the maccointrading seller on
ebay 
As we all know the only way to assess the value of the coin is to look at what they sell for, and I believe that's what they probably attempt to do most of the time.
That being said, MS65 is a stellar grade for this variety (and just in general) so I'm content enough with that coin alone to not regret sending them in. As for the few that downgraded, I got very good deals on all 7 coins to begin with, so I'm not all that disappointed, especially since two of the ICCS holders were falling apart and the seams starting to open up.
Curious what you think, or have other experiences on the same thing.