First and foremost it is worth noting that the verb "is" is mentioned in the Russian language much more often than "eat". First, due to the fact that it is a semantic dominant among a large number of synonyms (to eat, to eat, to devour, and so on). If the other person would not understand some of these words, the verb "is" in most cases, will eliminate the misunderstanding. Secondly, the word "is" has many other meanings, so it is familiar to more people and is commonly used.
The verb "to eat" is stylistically strongly restricted. In most cases it is used as a word that refers to a simple speech etiquette. Long with this verb the guests politely invited to the table. In modern Russian usage of the word is limited to the following cases.
- If you use the infinitive, part of the etiquette phrase.
- If you want to use the imperative mood.
- If the speaker appeals to children and, in some cases for young girls. To use this verb in the first person ("I eat) is only valid stylistically these two categories of people.
So if you don't want to make a mistake, use the word "is". It perfectly reflects the essential meaning and stylistically sound right in almost any situation.