He's against unbridled immigration.
So are most people.
That's literally it.
That's not
literally it at all. There are a whole range of things in which he's at odds with the current Pope.
This includes his views on proselytizing, particularly around other 'peoples of the book'.
He's claimed that a large percentage of the global population are in open apostasy (which, incidentally, I'd agree with).
He's taken a stand against any moves to ordain married men.
I'm not going to get into who is right and wrong in a theological sense. It's not really my place, and ultimately I'm not sure it moves anything in the 'right' direction. Burke would clearly see theological 'correctness' and the world moving in the right direction as being one and the same, but I don't have to.
However, they are vastly different in terms of their approaches to the church, and to how they think the church should approach the world. In many, many ways.