Hebrews vs. Egyptians (sounds familiar...)

It is difficult and even dangerous to draw strong conclusions out of a portion of a text before the intended message of its entirety is understood.
Therefore, in comparing the similarities and differences between Psalm 104 and the Egyptian "Hymn to Aten", I think it is important to make a few general observations first.

Both songs go into detail listing various aspects of nature; plants and animals, rivers and mountains, day and night. Both also have portions dedicated to declaring praises to their respective center of worship. Both nations who wrote these songs lived in a similar time and similar world, and both believed in a deity - in my estimation, they are both monotheistic, in that they are both credited with being the life-bringing force to all the earth.

Scholars have recognized these similarities and speculated that the songs may be related.

While I do not exclude that possibility, I think that the parallels are largely due to the basic shared poetic idea of praising God by observing His centrality to life in all forms. Thus, it doesn't seem strikingly significant.
Of course, there are also places where the songs differ, and it is these that I find worth studying.

The first point that came to my attention was how literal the Hymn of Aten is. It is obviously worshiping the literal sun. "You rise in perfection...upon the eastern horizon...", "Although you are far away, your rays are upon the land". There are sections that stray from this ("The earth comes forth into existence by your hand"). However, the more abstract description of Aten is preceded by what could almost be called a disclaimer: "You are in my heart, and there is no other who knows you except for your son (Nefer-kheperu-Re Wa-en-Re)". This brings another obvious difference, which is that the song very directly reaffirms the Pharaoh as king, and describes his reign over Egypt.

In the Hebrew Psalm, I recognized an abundance of direct action by God: "He makes his messengers the winds" (v.4), "He founded the earth on its solid base" (v.5), "You let lose the springs in freshets" (v. 10), "He makes the hay sprout" (v. 14), "The lions roar for prey, seeking from God their food." (. 21), etc. The references to His control over water and other things would not make much sense in the context of a sun-god. Also, it seems to be expressing that God is the cause, the actual driving force, whereas Aten was more of a facilitator, or the origin of life, though after that it flourishes on its own "[When day breaks] The entire land performs its work: all the flocks are content with their fodder, trees and plants grow, birds fly up their nests...they live when you rise for them."

The closing work of each song demonstrate their utterly different focus:

From the Hymn of Aten: "Eyes are upon your perfection until you set...you who rise and make everything grow for the King and everyone...because you founded the land and you raised for them your son... the King of Upper and Lower Egypt... and the  Foremost Wife of the King, whom he loves... living and young, forever and ever."

The Psalm, in contrast (beginning at v. 33): "Let me sing to the Lord while I live, let me hymn to my God while I breathe... Bless, Oh my being, the Lord, Hallelujah!"

In short, the possible parallels one can see in selected imagery is probably due to a similar trend of nature imagery for poetry, as well as both the sun and God being in some way life-giving. While the Egyptian song seems to focus on Aten as the powerful establisher of the king, the Hebrew poem is ultimately written to glorify God.