I have a feeling some of the coins i have in PCGS slabs would end up in a higher grade NGC slab.....should i crack out or send in for cross over?

First off, previously everytime i had a PCGS slabbed coin that i wanted in an NGC slab i would just send in for cross over.....i have found though that whenever i have done this they have never gone up a grade....or down a grade....they just always cross at the same grade.......do the graders at NGC see that PCGS graded a coin ms64 so they just do the same?? would it be more beneficial to crack the coins out of there PCGS slabs and submit as a raw coin with no grade? I have a couple of charlotte coins that although graded by PCGS to be AU58...with todays standards they could well be ms61-62 at NGC....if i submitted in the au58 slabs im sure they would come back au58....but then if i crack them out i loose any pedigree attached to the coin....decisions decisions....any ideas?

SMC

the attached image is of my favourite coin at the moment, pedigree to the Dingler & Elrod collections this 1856c is now at the top of the condition census after the owner of the finest coin decided to "brighten it up" and dip it...removing years of lovely patina....why in this day and age does a person think thats a good idea....a loss for the community! but i bonus for my client as his coin is now at the pinnacle of all 1856c's