Hi footballboy5571,
I have never shot the .300 Ultra Magnum, so I can't speak to its recoil. I have shot both .300 Winchester Magnums, .300 Weatherby Magnums, and the .350 Remington Magnum. In all honesty I couldn't differentiate much in a difference between them.
Alot has to do with the weight of the rifle, the design and material of the stock, and the load you are shooting. If all other things are equal, (ie. stock weight, stock composition, rifle weight),
and they seldom are, recoil will be determined by several factors. These factors are:
Bullet Weight
Bullet velocity
Bullet bearing surface
Powder burned to achieve velocity
As you change any of those factors you also change recoil. Somethings are constant. As bullet weight goes up...recoil impulse also increases. As the velocity increases....the speed which the recoil impulse occurs is also quickened. As bullet bearing surface is reduced....recoil impulse is reduced. And the more powder that is burned to achieve a particular velocity...the more recoil there will be!
How a person perceives recoil is a very subjective thing. Everyone has their limit or tolerance and once they exceed that limit.....their shooting accuracy will decrease. (Sometimes disasterously so!) To kind of get an idea for comparison sake, try this site:
http://www.chuckhawks.com/recoil_table_exp.htm
Hopefully this has helped!
P.S. As to your other question. Which one would make the best all around cartridge for hunting North America. Let me ask you this. Which is better...Apples or Oranges? Depending on who you ask you will get different answers to that question. And they can make logical arguments for their selection. But in the end......it is still Apples or Oranges. By the way.....for me it would be the .350 Remington Magnum!