Here are my preferred alternatives:
Qui sicut lupi agitant epulantur sicut di.
Par lupo venans dive epulatur.
Here's how I got there:
The relative clause seems more idiomatic to me. After all, one typically says qui tacet consentire videtur, not tacens consentire videtur. However, the construction with the participle is also perfectly correct.
"Like" in the sense here is regularly expressed with sicut, thus Qui sicut lupus agitat sicut deus epulatur. Frankly, I think the plural might sound even better ("like gods" is less awkward than "like a god"): Qui sicut lupi agitant sicut di epulantur. Note the nominative forms after sicut. Sicut is a conjunction, not a preposition, but the verb is understood in many situations, including this one--no need to repeat agitant or epulantur. Finally, I'd probably want to emphasize the nouns rather than the verbs, so I'd rearrange to Qui sicut lupi agitant epulantur sicut di.
Examples of sicut used in this way include Plagas sicut Thomas non intueor in Aquinas's hymn Adoro te devote, but looking sicut up in Lewis & Short you will find plenty of examples of this usage in Cicero, so it's definitely classical. I think it's fine to use par lupo to describe "[hunting] like a wolf"--it really means [hunting] equally with a wolf. I do not at all like par deo to describe "[feasting] like a god", since the point of "feasting like a god" is not that you are equal to the gods in feasting but that the feast in front of you is like a god's feast. Also, it seems awkward to have the adjective par modifying the same subject (venans [homo]) twice. So the closest to Joonas's translation that would sound right to me would be Par lupo venans epulatur sicut deus. If you want to keep it as brief as possible, you could probably say Par lupo venans dive epulatur.