Likelihood of crossover from one to the other is mostly directly correlated to your own grading ability.
I have had ICG slabbed coins that crossed to NGC (and some to PCGS). Some did not. I have had NGC coins rejected by PCGS; and I have had PCGS coins rejected by NGC.
A good guideline is the following:
1. Given a coin in a slab with grade M (M is whatever it is).
2. If the coin is PQ and has a chance of being graded M+n, then the coin is likely to crossover.
3. If the coin is a solid M, but not PQ, there is about an 80% likelihood of it crossing over.
4. If the coin is a borderline M (meaning it would be PQ if was graded M-n, then the likelihood of it crossing over is only about 20%.
5. If the coin is really M-n (it is overgraded), it is extremely unlikely to be crossed over.
For example: I recently viewed an image of a coin graded MS 67 Full Head with a STAR. I counted at least 6 dings between the kneecap and the foot - and the dings were clearly visible with the unaided eye. The grading team must have gotten carried away with the toning because coins with a couple of dings (sometimes only one)across the shin are usually graded MS64. 6 dings normally results in MS 63. I would be willing to bet that if I bought that coin and cracked it out and resubmitted to the very same service, it would come back as either MS64 FH or MS65 FH.
So, (1) if you believe the coin is overgraded, don't waste your time trying to crack it or crossover - unless you want to bet that the service grader is less qualified than you. (2) if you believe the coin will always grade M and has a chance at M+n (higher grade), then play the crack out game or cross it over.
I had a bunch of coins in XYZ holder: Those I really thought were undergraded, I cracked and submitted some to PCGS and some to NGC. Those I thought were properly graded, I submitted some to PCGS and some to NGC for crossover. Those I felt were either marginal or were overgraded, I sold at a discount to get rid of them.
So, does your "perfect" coin in that ICG MS70 holder exhibit one or more tiny nicks (flashes bright when rotated); or perhaps a small dimple in the planchet; or maybe a very small scuff mark; or perhaps a small, round (but perfect) spot? If so, then although they are obviously "perfect" defects and so are not defects at all, don't try the crossover game.
I've seen PR68 coins that look better than some PR70 coins. In fact I owned some of both -- until I gave up trying to put together a set of PR70 graded coins that did not have any of the aforementioned "perfect defects" visible with a 3x or 5x loupe.
Just my opinion.