What's the difference between "Chłowiek jest zwierzęciem" and "Chłowiek to zwerzę"?
Both means "the human is an animal"
"Człowiek jest zwierzęciem" is more likely do be understood as applying biological systematics (human is neither bacteria nor plant, it belongs to the systematic group of animals).
"Człowiek to zwierzę" is more likely to be understood as a derogatory opinion about mankind.
"Człowiek jest zwierzęciem" sounds more elegant that "Człowiek to zwierzę", but the difference is too small to bother. Just use the "noun + to + noun" construction with both nouns in nominative, like jmango2 said.
I don't think there's a difference in meaning, as far as I can tell.
But in terms of grammar, using the verb być (jest) means you have to use the instrumental case.
If you just use to, then you can have both nouns in the nominative case, which might be easier for English speakers at first.