As far as I know yes, they are the most strict while grading
US coins.
People tend to rate the third party graders in order of highest premium for the slab as PCGS, NGC and finally ANACS... Which would indicate to me that PCGS is the strictest if they bring the highest premium. More so because they have lower populations of the given grades. Which again would indicate the strictest grading.
Also you have to remember that all of the top 3 third party graders are wrong at times... I have coins in all three company's slabs, and I have some that I believe are both under and overgraded... Always remember buy the coin and not the slab. Grading is soooo subjective that honestly (just for the sake of mentioning) you could crack out all of your slabbed PCGS coins and resubmit them to PCGS and there's still no guarantee they will grade the same, actually theres probably a pretty good chance they could come back different.. some could come back lower or higher.... Or the same... All subjective. It depends on who's grading them, If they got cut off in traffic on the way to work, fighting with the wife, just won the lotto, the rarity of the coin (I believe they are less strict on certian coins/dates/mints) etc...
Personally I prefer to cherrypick raw examples... (But I will buy all three third party graded slabbed coins if I like the toning, designation etc) but for raw coins I buy empty slabs identical to the PCGS slabs and label them myself (never for resale). But my albums are a mix of all three top
TPG'ers as well as my own slabs.. Would I like them all the same.. I guess that would be cool, and look good, but it's the coin in the slab I look at, not the label so I could care less if all the slabs match.. I have super OCD also, lol, but not towards my slabs.. More so towards my coins..
Unless your collecting "slabs" try to remember to buy the coin and not the slab, that's probably one of, if not THE most important sayings in coin collecting... Wether PCGS, NGC, ANACS or RAW always buy the coin that stands out to you, your personal tastes, and grade it yourself..
Cross grading is fine, I just wouldn't expect them to all cross the same.. But this is likewise if you were to cross submit to any of the top 3
TPG'ers... There's no guarantee that if you sent all your PCGS slabs to NGC they would cross the same either... So on so forth.. No guarantee whatsoever. But if you get pretty good at grading yourself you can probably pick coins you think would "make the grade"...