Why is it that when one takes a high quality multi-vitamin, the urine turns
a more pronounced yellow?

Simple enough. The urine is colored by excess Vitamin B-2.

Also, it is a good indication that you are NOT drinking enough water.

Is there really any difference between the typical vitamin you can buy
at the grocery store and those distributed by ‘quality’ companies such as
Nature Sunshine, Nutrition for Life, Herbal Life, Shaklee, and Amway? If
so, is it really worth the price difference.

Look at the labels. Most of the high quality multis have more
ingredients: multiple sources of A, C, and E; trace minerals like
selenium; trendy new nutrients like Coenzyme Q-10. They also have
higher levels of B vitamins, most of which are relatively inexpensive.
Those B vitamins probably account for the coloring you spoke of.

I beg to differ about your definition of a ‘quality’ company. Certainly
there are cheap vitamins. But, many companies sell vitamins that are more
than good enough. In my opinion, those quality companies are just scamming
the public with this nonsense about quality and better bio-avialability.