Tire feedback when cornering
Knobs and pavement don't go together. At all. Knobs are made to dig into loose riding surfaces to optimize traction. They can't do that on pavement and, among other reasons, that's why road tires don't have knobs. 

What you're likely feeling with the higher profile knob is more warning before the tire cuts loose. The lower profile knobs on the Land Cruiser almost certainly grip pavement better, but offer less warning before they let loose.

The best tire for grip on pavement is a slick. Slicks offer the most rubber in contact with the pavement and the least deformation under side load. The flip side to that coin is that when they're ready to cut loose they offer virtually no warning, and when they're gone they're gone- your chances of recovering traction are nearly zero.

To kind of answer your bonus question, cornering techniques don't differ so much by tire, but by riding type. There are differing cornering techniques for road vs mountain bike riding. I would say that cornering on dirt is much more dynamic than on pavement.

EDIT: in response to your question in the comments:


  So basically my question was "[Your third paragraph] - is that normal?" and the answer is "Yup, deal with it."?


In terms of your tire cutting loose, the answer is partially yes, but not entirely. Proper cornering technique and weighting of your bike, especially your front tire, will help you maintain traction. Keep in mind that it's different for road than it is for mountain, but that's a different question.

A set of tires specifically designed for pavement would make a huge difference. You're not limited to narrow road slicks either. The Specialized Electrak is very wide for a slick, and Schwalbe has several very wide mostly slick tires that can be run at very low pressures (as in, 20-30psi) which equals a lot of rubber on the road and a lot of traction.

In the end though, when you lose the front end on the road it is going to be harder to recover for a variety of reasons. It's not the same as temporarily losing traction in the dirt because you hit an especially loose corner. Traction on the pavement is typically pretty consistent, and you're usually going significantly faster, so when the front tire lets go, it will be very hard to regain traction and stand the bike back up. The tips above will help with the problem but not eliminate it.