"To eat up" is "aufessen" as far as I understand. "Aufessen" is no insult. My mother said: "Du musst aufessen!" or "Du musst deinen Teller leer essen!"
This might be wrong in long terms because of the weight but is no insult.
"Auffressen" is coarse (insulting) in this context when applied to human beings. No mother ever would say to her child: "Du musst deinen Teller leerfressen." or "Du musst auffressen!"
"Fressen" - when applied to human beings is mostly an insult.
"Du frisst wie ein Schwein!" - here you have the direct comparison to an animal. It means you are not eating normally but the meal lands partly on the table and on your skirt. You may eat too fast and too much but mostly this is related to the behavior during eating. This is very insulting.
Du isst nicht - du frisst!
This is also an insult but related to the high amount and sometimes to the high speed of eating.
There is one fixed idiom I know, where it is no insult, but neither it is "educated" speaking:
"Wann gibt's endlich was zu fressen?" - coll. and not to be used if you are not really very hungry.
It means: "I'm hungry. When the hell will I get my meal?" (I did not translate the style here.)
Another idiom is a hint to a child:
"Friss nicht, iss anständig!"
"Do not eat like an animal, eat like an educated human being."
"Seinen Kummer in sich hineinfressen" - here "fressen" is appropriate and not coarse. To suffer sorrows and tell nobody. (Can I say so in English?)
There was a change in usage during the last 100 years.
Grimms "Deutsches Wörterbuch"
http://germazope.uni-trier.de/Projects/WBB/woerterbuecher/dwb/... states:
fressen ist aufessen, verzehren, ganz verschlingen, vorare, devorare, während essen häufig den partitivbegrif hat und davon essen ausdrückt, also oft den gen.(Genuss) der sache erfordert (gramm. 4, 649), fressen fast nur den acc. da nun die thiere das ihnen hingeworfne futter, die ihnen zu theil gewordne speise verschlingen und verzehren, so bezieht sich auf sie die stärkere, rohere vorstellung des fressens.
Note: Grimm used an old spelling. He states "Fressen" is to eat up, to consume, to engorge. "Essen" requires enjoyment, while "fressen" was just the mechanical part.
das thier friszt, der mensch iszt, und erst wenn er thierisch einschlingt, wird ihm auch fressen beigelegt, Nebucadnezar, wild geworden, frasz gras wie ochsen. Dan. 5, 21. begreiflich erfährt dieser sprachgebrauch viele ausnahmen und oft heiszt es von thieren, besonders kleinen, zierlichen, dasz sie essen, wie umgekehrt fressen von menschen gilt im sinne des verzehrens, aufzehrens.
Already in this time Grimm states the usage "Der Mensch isst, das Tier frisst."
But he also states a lot of exceptions.
Sometimes "essen" is also used for animals - especially if they are small and cute, (I would say like pets).
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"Fressen" is also used in some other contexts, "(sich einfressen" "Der Fluss frisst sich in den Boden ein.")
"Zerfressen" "die Oberfläche ist ganz zerfressen."
