This question may be better for Snopes.

The quotes are almost certainly apocryphal, in keeping with a long history of military apocrypha, and should be interpreted as humor but not as an authenticated quote. I have located two publications which refer to the quote without being able to directly attribute it:

An online article from The Diplomat, Unorthodox and Chaotic: How America Should Fight Wars, by James R. Holmes from September 27, 2013 references the quotes, opining they are probably apocryphal.

Taking your soviet quote, I searched google scholar and located a few candidates, though none were before the 1990's.

<a href="http://cgsc.contentdm.oclc.org/cdm/singleitem/collection/p124201coll1/id/1205/rec/15" rel="nofollow">Army Military Review Article Here</a>, footnotes as source not given.

The earliest published source was doctoral dissertation by a Lt. Col. in 1994, who sourced it as (From a Russian document. This quote found on a U.S. Army office wall.) I've got to go pick up my kid but will give additional info as a follow up with a link to the dissertation.

These are not genuine historical quotes, however there is some truth in terms of symbolism.

A reflection of their totalitarian ideologies, the Germans and USSR practiced a strict and rigid top down command structure where lower ranking individuals were restricted from making critical decisions. Given the volatility of the situation on the battlefield, this was often to the detriment to their ranks, as they would be unable to act quick enough to enemy moves.

An exemplary example would be the Germans unable to respond to D-Day with their armored reserves because Hitler was sleeping and no one wanted to wake him.

In contrast, the allies put a lot more faith in their lower ranking commanding officers. Letting the generals and colonels dictate strategy on the maps, but allowing the captains and lieutenants take control tactically on the battlefield. As a result their forces were much more dynamic and able to respond to threats quicker with independent control rather than having to wait for the approval from a general 400 miles away.

Gilbert, Martin (1989). The Second World War: A Complete History. New York: H. Holt.

"The Elimination of the Alternatives. Jul–Aug 1942". US Army in WWII – Strategic Planning for Coalition Warfare