Again, Steve, - it’s not private if one says it at a public campaign rally-— perhaps you’re trying to convey something else.
As for your point that Trump is stronger than Cruz on immigration— that appears to be the significance of Cruz’s current comment-— if Trump is going to bring back illegals, while Cruz is not— Trump’s position is no longer stronger than Cruz’s- look for Cruz to call it amnesty.
It’s private in that it’s a one-on-one and not on the stump. Cruz has yet to make these statements ‘public’. If/when he does then it’s game on.
As far as who wins the war on immigration Cruz is going to have an uphill battle here. Since July Trump has owned this issue and has branded it TRUMP. Cruz hitting him on this and then going harder than Trump may not be enough in the end, but time will tell.