Here are some anecdotes:
Several years ago I submitted a batch of 20 PCGS of a better date G1/20 that had came from a single sheet. I sent them through NCS first and I think about 17 crossed to NGC MS69 and 3 fell down to NGC 68. Although the crossover rate was ok, I'm not sure it was worth the money. But, it was cheaper for G1/20 back then, and I think I took advantage of some sort of grading special. Also, there was a miscommunication, because if the coins wouldn't cross, I didn't want them taken out of PCGS 69 and put into NGC 68, but it was part of a few groups of coins that I sent in, so I think the clerk got confused.
I've sent some stray G1/2 in for crossover. I'd say perhaps 6 of 10 crossed PCGS 69 to NGC 69. Perhaps 3 of 10 did not cross. And then the surprise. I sent one G1/2 in that was a PCGS MS69 and it came back a NGC MS70! I've attached the PCGS file image. The PCGS file photo has a noticeable red spot (which kept it no higher than a 69), but otherwise had a nice forehead. Since I sent it through NCS first, the spot was eliminated, and I guess the NGC graders then liked what they saw.
Overall, if I had not sent the majority of these coins through NCS first, I'm certain that the cross over rate would be lower. Also, I was somewhat selective in what I sent in. I screened the coins and decided some PCGS 69s were not in good enough condition to try. As time goes by, and there has been a preference for NGC for years, I would guess that many of the PCGS graded coins that are still on the market (that aren't in brand new holders) have already had someone look at them to see if they would cross over. I pretty much assume that if it is an older PCGS holder on eBay it probably isn't in good enough condition to have a good chance of crossing over. Otherwise, someone would have tried already. Something to keep in mind.
Take home message: If I saw an otherwise lovely PCGS 68 or PCGS 69 that has red spots that are present in the PCGS file photo (so they were there at the time of grading), I would not hesitate to send them through NCS and then to NGC grading. From what I heard, however, I wouldn't try crossing over PCGS 70 to NGC 70. Although I'm not sure I've ever bought a PCGS 70.